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Copyright N° 



COPYRiGHT DEPOSIT. 



SURVEYING AND TABLES 



BY 

G. A. WENTWORTH 

Author of a Series of Text-Books in Mathematics 



SECOND REVISED EDITION 



BOSTON, U.S.A. 

GINN & COMPANY, PUBLISHERS 

CI)e SltbcnaE-ttm ^Jress 

1903 



THE LIBRARY OF 
CONGRESS. 

Two Copies Received 

OT 16 1903 

Copyright Entry 
CLASS Cc XXc. No. 

S U- k / 3 

COPY B. 



MATHEMATICAL TEXT-BOOKS 

BY 

GEORGE A. WENTWORTH 



Elementary Arithmetic 

Practical Arithmetic 

Mental Arithmetic 

Primary Arithmetic (Wentworth and Reed) 

Grammar School Arithmetic 

Advanced Arithmetic 

Exercises in Arithmetic (wentworth and Hill) 

First Steps in Algebra 

School Algebra 

New School Algebra 

Higher Algebra 

Elements of Algebra 

Complete Algebra 

Shorter Course in Algebra 

College Algebra (Revised Edition) 

Exercises in Algebra (Wentworth and Hill) 

First Steps in Geometry (Wentworth and Hill) 

Plane and Solid Geometry (Revised) 

Plane Geometry (Revised) 

Solid Geometry (Revised) 

Plane and Solid Geometry and Plane Trigonometry 

(Second Revised Edition) _ * 

Analytic Geometry ' ' , 

Logarithms and Metric Measures 
Geometrical Exercises 
Syllabus of Geometry 

Examination Manual in Geometry (Wentworth and Hill) 
Exercise Manual in Geometry (Wentworth and Hill) 
Plane Trigonometry (Second Revised Edition) 
Plane Trigonometry and Tables (Second Revised 

Edition) 
Plane and Spherical Trigonometry (Second Revised 

Edition) 
Plane and Spherical Trigonometry, and Tables 

(S0c(jn'd Revised Ed'itior) 
Plane 'pigpaomptry and Surveying, and Tables 

/'Second Revised Edition) 
Surveying and Tables (Second Revised Edition) 
Plane and Spherical Trigonometry and Surveying, 

and T§.biis t (Seoo c nd Revised Edition) 
Plaice ard ,'Sphencal Trigonometry, Surveying, and 

Navigation (Second Revised Edition) 
Logarithmic and Trigonometric Tables 

Seven Tables (Wentworth and Hill) 

Complete 



Copyright, 1882, 1895, 1896, 1903, by 
G. A. WENTWORTH 



ALL EIGHTS RESERVED 



l-tQ0g(a 



PREFACE 

The object of this work on Surveying is to present the subject in 
a clear and intelligible way, according to the best methods in actual 
use, and in so small a compass that students in general will find 
time to acquire a competent knowledge of this important study. 

The author is under obligation to G. A. Hill, A.M., of Cambridge, 
Mass. ; to Professor James L. Patterson, of Chestnut Hill, Pa. ; to 
Dr. F. N. Cole, of New York, N.Y. ; to Professor S. F. Norris, of 
Baltimore, Md. ; and to Professor B. F. Yanney, of Alliance, Ohio. 
Professor Yanney has done most of the work on the second revision, 
and Miss M. Gertrude Cross, of Boston, has furnished the drawings. 

G. A. WENTWORTH. 
Exeter, N.H., 1903. 



CONTENTS 

SURVEYING 

[ The numbers refer to the pages.] 

CHAPTER I. Field Instruments : 

Definitions, 1 ; classification, 1 ; operations comprised, 2 ; the sur- 
veyor's chain, 3; the engineer's chain, 3; accompanying pieces, 4; 
how to chain, 4 ; special constructions by means of the chain, 5 ; 
obstacles to chaining, 7 ; the tape, 9 ; the compass, 10 ; kinds of 
compasses, 11 ; bearing of a line, 12 ; checking bearings, 13 ; obsta- 
cles, 14 ; measurement of horizontal angles, 14 ; measurement of 
vertical angles, 15 ; verniers, 15 ; uses of the compass vernier, 17 ; 
magnetic declination, 19 ; surveyor's transit, 23 ; uses, 24 ; measure- 
ment of horizontal angles, 26 ; measurement of vertical angles, 26 ; 
stadia measurements, 26 ; the solar compass, 28 ; to establish a true 
meridian, 32 ; the Y level, 36 ; the leveling rod, 36 ; substitutes for 
the Y level, 39 ; the plane table, 40 ; to orient the table, 42 ; to plot' 
any point, 43 ; to plot a field, 43 ; the three-point problem, 44. 

CHAPTER II. Office Instruments : 

Definitions, 46 ; the diagonal scale, 46 ; the circular protractor, 47 ; 
constructions, 48 ; the planimeter, 49 ; the slide rule, 49. 

CHAPTER III. Land Surveying: 

Definitions, 50 ; special methods of surveying, and of computing 
areas, 51 ; rectangular system of co-ordinates, 52 ; general method 
for farm surveys, 57 ; field notes, 58 ; computation of the area, 58 ; 
balancing the work, 60 ; supplying omissions, 61 ; to make a plot, 
63 ; modification of the latitude and departure method, 66 ; location 
surveys, 67 ; illustrative problems, 67 ; laying out the public lands, 
71 ; reference lines, 71 ; townships, 71 ; subdivision of townships, 
73 ; meander lines, 73. 



vi CONTENTS 

CHAPTER IV. Triangulation: 

Definitions, 74 ; classification, 75 ; measurement of base lines, 75 ; 
measurement of angles, 76. 

CHAPTER V. Leveling: 

Definitions, 77 ; corrections for curvature and refraction, 77 ; dif- 
ferential leveling, 78 ; single setting of the level,' 78 ; several settings 
of the level, 79 ; profile leveling, 80 ; field work, 81 ; making the 
profile, 84 ; topographic leveling, 85 ; drainage surveying, 86 ; field 
work, 86 ; plot and profile, 86. 

CHAPTER VI. Railroad Surveying : 

Laying out the route, 89 ; establishing the roadbed, 89 ; excava- 
tions, 89 ; embankments, 90 ; curves, 91 ; methods of laying out the 
curve, 92. 

CHAPTER VII. City Surveying: 

■4 

Eield-work instruments, 94 ; streets, 94 ; blocks and lots, 96 ; plots, 
96 ; records, 96. 



SURVEYING 

CHAPTER I 

FIELD INSTRUMENTS 

SECTION I 

DEFINITIONS 

Definition. Surveying is the art of determining and repre- 
senting distances, areas, and the relative position of points on 
the surface of the earth. 

Classification. Of surveying there are various kinds, depend- 
ing upon the extent, the purpose, or the method of the survey. 
The following are the principal divisions : 

1. Plane Surveying, in which the part of the earth's surface 
surveyed is regarded as a plane ; Geodetic Surveying, in which 
the true figure of the earth is regarded. 

2. Land Surveying, in which boundary lines, contents, and 
outline maps are the chief things aimed at ; Topographic Sur- 
veying, in which differences in elevation and contour maps are 
chiefly sought ; Hydrographic Surveying, in which the purpose 
is to determine the configuration and topography of the bed or 
basin of a body of water ; Mine Surveying, in which the posi- 
tion and extent of underground excavations are determined and 
graphically represented. 

3. Rectangular Surveying, in which a system of perpen- 
dicular lines is used as reference lines ; Triangular Surveying, 
which proceeds by means of a system of triangles referred to 
a well established base line. 

1 



2 SURVEYING 

Operations Comprised. Surveying commonly comprises the 
following three distinct operations : 

1. The Field Measurements, or the determining certain lines 
and angles by direct measurement. 

2. The Computation of the required parts from the meas- 
ured lines and angles. 

3. The Plotting, or representing on paper the measured and 
the computed parts in relative extent and position. 

Historic Note. Surveying is undoubtedly one of the oldest of the arts 
of civilized man. The Bible contains several admonitions not to 
remove " the ancient landmark," as in Proverbs xxii. 28. To the Baby- 
lonians is credited the division of the circle into 360 degrees. The Egyp- 
tians were known to survey frequently the valley of the Nile, a necessity 
owing to the periodic overflow of that river. Thence came Geometry. The 
Egyptians also possessed rules for finding the area of land of various shapes. 
Moreover, on Egyptian soil the Greek mathematician Eratosthenes made 
the first attempt at determining the circumference of the earth by meas- 
uring an arc of the circumference. This was in 276 b.c. Among the 
Romans Surveying was considered one of the liberal arts, and received 
impetus in the time of Julius Caesar from his sweeping order that the 
entire empire should be surveyed for the purpose of equitable adjustment 
of taxes, and also from the introduction of the more practical parts of 
Greek Geometry. The works of Roman surveyors served as models for 
centuries, and much that we have to-day is only improvements on what has 
been handed down from them. For a brief account of surveying in the 
United States, see Cajori's " The Teaching and History of Mathematics 
in the United States," pp. 92, 286. 



FIELD INSTRUMENTS 3 

SECTION II 
THE CHAIN 

Surveyor's Chain. The Surveyor's Chain, or G-unter's Chain 
as it is often called, is made of iron or steel wire and is 4 
rods or 66 feet long, composed of 100 links connected by small 
rings, and provided with a tally mark at the end of every 10 
links. A link as a unit of measure includes a link of the chain 
and half the rings that connect it with adjoining links. Each 
link is 7.92 inches long. Since a chain is 4 rods long, a square 
chain contains 16 square rods, and since an acre contains 160 
square rods, a square chain is one-tenth of an acre. A square 
chain contains also 10,000 square links and, therefore, an acre 
contains 100,000 square links. Hence, if a given area is 
expressed in square chains, it is reduced to acres by pointing 
off the last figure, and, if expressed in square links, it is reduced 
to acres by pointing off the last five figures. The tally marks 
are appropriately notched to facilitate counting links from 
either end, the one at the middle of the chain being rounded 
so as to be distinguished readily from the others. Handles 
form part of the end links, to which they are so attached as 
to prevent twisting and to allow lengthening or shortening 
of the chain. The Surveyor's Chain is used in measuring 
land. 

Engineer's Chain. The Engineer's Chain differs from the 
ordinary Surveyor's Chain chiefly in that it is 100 feet in 
length, the length of each link being 1 foot. It is used in 
surveying railroads and canals, and often in other surveys 
where extensive lines are to be run. 

Both the Surveyor's Chain and the Engineer's Chain are 
generally provided with attachments, so that from the full 
chains half-chains can be made up, to be used in case of rough 
or hilly country. 



4 SURVEYING 

Accompanying Pieces. Usually eleven, sometimes ten, Mark- 
ing pins go with the chain. These are of iron or steel, about 
14 inches long, pointed at one end and formed into a ring at 
the other end. In case eleven pins are used, the first one is 
placed at the beginning of the line to be measured, and there- 
after one at the end of each chain. The last pin in the ground 
is, therefore, not to be counted. In case ten pins are used, 
the first one is placed at the end of the first chain, and so on, 
the last pin in the ground being counted. Strips of red cloth 
should be fastened to the ring ends of the pins so as to make 
them easily visible. Ranging poles, which are of various 
lengths, are necessary for alignment. These are commonly 
made of wood, and are steel shod, graduated to feet, and 
painted in alternate red and white stripes. 

How to chain. Ranging poles should be placed, one at each 
end of the line to be measured, and' at such intermediate 
points as the necessities of the case require. A head chain- 
man or leader, and a rear chainman or follower are required. 
The follower takes one end of the Chain, and one pin, which 
he thrusts into the ground at the beginning of the line. The 
leader takes the other end of the chain and the remaining ten 
pins, and moves forward until the word " Halt " from the fol- 
lower warns him that he has advanced nearly the. length of 
the chain. At this signal he stops, and the follower, mean- 
while having placed his end of the chain against the pin at 
the beginning of the line, directs the leader by the words 
" Right" and "Left" until he is exactly in the line. This 
being accomplished, and' the chain tightly stretched in a hori- 
zontal position, the follower says, " Down." The leader then 
puts in a pin at the end. of the chain and answers, "Down" ; 
after which the follower withdraws the pin at his end of the 
chain, and the chainmen move forward, repeating the process 
just described until the end of the line is reached. 

If the marking pins in the hands of the leader are all placed 



FIELD INSTRUMENTS 5 

before the end. of the line is reached, after putting the last pin 
in the ground he waits until the follower conies up to him, 
gives him the ten pins in his hands and records the fact that 
ten chains have been measured. The measuring then proceeds 
as before. If the distance from the last pin to the end of the 
line is less than a chain, the leader places his end of the chain 
at the end of the line, and the follower stretches tightly such 
part of the chain as is necessary to reach the last pin, and 
the number of links is counted. If the ground slopes, one end 
of the chain must be raised until the horizontal position is 
attained. By means of a plumb line or a slender staff or, less 
accurately, in case of the leader by dropping a pin (heavy end 
downwards), the point vertically under the raised end of the 
chain may be determined. If the slope is considerable, half 
a chain or less may be used ; in which case care must be taken 
that the correct number of full chains and links is found. For 
instance, if a tally shows 15 half chains and 35 links, the 
appropriate measure is 7 chains and 85 links, or, as it is 
usually expressed, 7.85 chains. 

Special Constructions by Means of the Chain. 1. At a given 
point in a given line to construct a perpendicular to that 
line. 

Let LE (Fig. 1) be the given line, and P the given point. 
On LE measure off PB = PA = 20 links. Then place one end of 
the chain at B and the other end at A. 
Stretch the chain from the middle point, 
and mark that point, as C. PC is the 
perpendicular required. (Why ?) 

Or, make PB = 30 links. Place one 







E 



A P B 

end of the chain at P, and the end of ' 

Fig. l 

the 90th link at B. Then, taking the 

chain at the end of the 40th link from P and stretching 
both portions tightly, mark that point, as C. Then PC is the 
perpendicular required. (Why ?) 



6 



SURVEYING 



2. Through a given point without a given line to construct 
a perpendicular to that line. 

Let LE (Fig. 1) be the given line, and C the given point. 
Take any point as B in the line and stretch the chain between 
C and B ; then swing the chain about C until the point at B is 
again in the line, as at A. Measure the distance between A 
and B. Then P, the mid-point of AB, is a second point in the 
required perpendicular. (Why ?) 

Or, let the middle of the part of the chain between C and B 
be held in place, and swing the end at C until it meets the 
line as at P. PC is the required perpendicular. (Why?) 

3. At a given point in a given line to construct an angle 
equal to a given angle. 





Let P (Fig. 2) be the given point in the given line LE, 
and angle A the given angle. Make PD = AB. At D and B, 
respectively, construct perpendiculars DF and BC. Make 
DO = BC. Then angle OPD is the angle required. (Why ?) 

4. To construct any given angle, as 25° 40'. 

Find from the tables the tangent of 25° 40', which is 0.4806. 
Lay off PD (Fig. 2) =100 links. Construct the perpendicular 
DF and lay off DO = 48.06 links. Then angle OPD is the 
angle required. (Why ?) 

5. Through a given point to construct a line parallel to a 
given line. 

Let P (Fig. 3) represent the given point, and LE the 
given line. Through P lay out any convenient line as BA 



FIELD INSTRUMENTS 7 

intersecting LE. Construct angle BPB = angle PAE. Then 
the line CD is the required line. (Why ?) 



E 



A 




IT 



D 



E 



Fig. 3 

Obstacles to chaining. In general practice various obstacles 
are encountered in chaining. The circumstances in each case 
must decide the best method to be used. Only a few sugges- 
tive cases can be considered in this work. 

1. To measure a line when a building, or other object, 
stands in the way. 

In Pig. 4 construct the 
perpendicular AB, the per- -^— 
pendicular BC, the perpen- 
dicular CD = AB, then the 
perpendicular DE, which fig. 4 

will be in line LA prolonged. 

Then, LA + BC + DE = LE. (Why ?) As a check, another 
series of perpendiculars may be constructed. 

2. To measure across a body of water. 

At A (Fig, 5) lay 

out AP, making angle 
^£ = 60°. This can 
be done by laying out 
the equilateral tri- 
angle ABB. At P 
range out PC, mak- 
ing angle APC = 60°. 
Then measure AP. 




8 SURVEYING 

The line AC is equal to AP. (Why ?) If C is some fixed 
point in LE, across the stream, accessible or inaccessible, we 
may proceed as follows : After laying out AP, as already 
described, with 90 links of the chain stretched in the form 
of an equilateral triangle, and with one side of this triangle 
in AP, move the triangle until the point C is in line with 
the forward side of the triangle. Then proceed as before. 

3. To measure a line the end of which is invisible from 
the beginning, and the intermediate points are unknown. 

C 

l d; e 



B ~~^~-J L 



R 



Let LE (Fig. 6) represent the line. Lay out the line LR so 
that; R shall be beyond E and visible from L. Construct 
from E the perpendicular EA to LR. Measure LA and AE. 
LE can then be computed. (How ?) If intermediate points 
on LE are to be sought, take any point in LA, as B ; construct 
BC perpendicular to LA ; then measure off BD of such length 
that BD : AE = LB : LA The line LR is called a random 

T e line. 

4. To measure the dis- 
tance between two inaccessi- 
ble points. 

Let L and E (Fig. 7) be 
two inaccessible points. 
Select some point as P from 
which both L and E are 
,' visible. Measure PL and PE 
by the method in 2. Eange 




E' 



FIELD INSTRUMENTS 9 

out PL' in line with LP and equal to L,P ; similarly, RE' = ER. 
Then measure L'E', which is equal to LE. (Why?) 

EXERCISE I 

1. Range out a line which, by estimation, is more than 
10 chains long. Then measure it with the chain out and 
back. 

2. Prolong a line beyond a building, or other obstacle which 
prevents continuous alignment. 

3. Find the distance from a point to a line when the dis- 
tance is more than a chain. 

4. Lay out a square field each side of which shall be 5.76 
chains long. 

5. Find the length of a line by means of a random line. 
Then, as a check, find its length by direct measurement. 



SECTION III 
THE TAPE 

Kinds of Tape. The tape measure used by the surveyor 
or engineer consists of a thin ribbon of steel, or of linen 
with interwoven wires of brass, wound upon a reel, often in 
a leather or metal case. Tapes vary in length from 25 feet 
to 500 feet or more. They are variously graduated to links, 
to feet and inches, to feet and tenths of a foot, to metric units, 
or to a combination of these. A common combination is feet 
and tenths of a foot on one side, and links on the reverse side. 

Uses. The kind of tape determines to a great extent the 
use to which it is to be put. If 33 feet or 66 feet long and 
graduated to links, the evident purpose is for land survey- 
ing. If 50 feet or 100 feet long and graduated to feet and 



10 



SURVEYING 



tenths of a foot, the tape is especially designed for city work. 
Other kinds are employed in bridge, road, or mining work, in 
very accurate measurements of base lines, or as standards of 
comparison for other instruments of measurement. 



SECTION IV 

THE COMPASS 

Parts and their Uses. The essentials of the compass, one 
style of which is shown in Fig. 8, are : the compass circle, 
graduated to half degrees and figured from 0° to 90° each way 




Fig. 8. The Surveyor's Compass 

Note. The letters E and AV on the face of the compass are reversed 
from their true positions. The reason for this is that if the sights are 
turned towards the west, the north end of the needle is turned towards 
the letter W, and if the north end of the needle is turned towards E, the 
sights are turned towards .the east. 

If the north end of the needle points exactly towards E or W, the 
sights range east or west. 



FIELD INSTRUMENTS 11 

from the north and south points, for indicating the directions 
of lines ; the magnetic needle, pivoted on a pin at the centre 
of the compass circle, for showing the direction of the mag- 
netic meridian ; and the sight standards, attached to the ends 
of the main plate, for alignment. To the main plate are 
attached two spirit levels at right angles to each other for 
leveling the instrument; underneath is a needle-lifting screw 
which, by actuating a concealed spring, lifts the needle from 
the pivot and presses it against the glass covering of the 
compass circle when the instrument is not in use ; a tangent 
screw, and almost directly under it a clamp screw, which 
operates the vernier; and a small dial plate for keeping tally 
in chaining. The north end of the needle usually has some 
ornamentation to distinguish it from the south end, and a 
coil of fine wire is wound on the south end to prevent the 
needle from dipping. The sight standards have fine slits 
nearly their whole length, with circular openings at intervals 
to facilitate sighting upon an object ; on the edges of the north 
standard are tangent scales for reading vertical angles, and 
on the outside of the south standard are two eyepieces at the 
same distance from the main plate as the zeros of the tangent 
scales, respectively. The telescopic sight is an attachment to 
the south standard, now often used. The instrument entire 
turns horizontally upon the upper end of a ball spindle, the 
lower end of which rests in a spherical socket in the top of 
a Jacob's staff, or a tripod, which supports the instrument. 
The socket of the compass which fits to the ball spindle is 
provided with a clamp screw and a spring catch. From the 
centre of the plate at the top of the tripod a plummet is 
suspended by which the centre of the compass can be placed 
directly over a definite point on the ground. 

Kinds of Compasses. The compass described is the vernier 
compass, or surveyor's compass, and is the one in general use. 
If there is no vernier attachment, the compass is called a plain 



12 



SURVEYING 



compass and is used in running new lines and the preparation 
of maps. A railroad compass has all the features of the vernier 
compass, and has also a vernier plate and graduated limb for 
measuring horizontal angles. 

Hints on the Use and Care of Instruments. The instruments 
described in this work are adjusted by the maker. If they 
should require readjustment, full directions will be found 
in the manual furnished with the instruments. Before begin- 
ning to use any instrument, make a thorough study of its 
various parts and their uses. In moving or adjusting any 
part always know what you are doing and why you are doing 
it. When an instrument is not in use keep it in a place that 
is free from moisture and dust. 

Bearing of a Line. The magnetic meridian of a place is the 
direction which a bar magnet assumes when freely supported 

in • a horizontal position. 
The magnetic bearing of a 
line is the angle it makes 
with the magnetic merid- 
ian. To take the bearing 
of a line proceed as fol- 
lows : Place the compass 
so that the Jacob's staff, 
or plummet of the tripod, 
is directly over one end of 
the line, and level by press- 
ing with the hands on the 
main plate until the bub- 
bles are brought to the 
centres of the spirit levels. 
Turn the south end of the instrument toward you, and sight 
at the ranging pole at the other end of the line. Read the 
bearing from the north end of the needle. First, write N. or 
S. according as the north end of the needle is nearer N. or S. 




Fig. 9 



FIELD INSTRUMENTS 13 

of the compass circle ; secondly, write the number of degrees 
between the north end of the needle and the nearest zero mark ; 
thirdly, write E. or W. according as the north end of the needle 
is nearer E. or W. of the compass circle. Thus, in Fig. 9 (a), the 
bearing is K 45° W. ; (b), N. 60° E. ; (c), S. 60° W. ; (d), S. 45° E. 

If the needle coincides with the N.S. or E.W. line, the 
bearing is N., S., E., or W. according as the north end of the 
needle is over N., S., E., or W. As the compass circle is 
divided into half degrees, the bearing may be determined 
pretty accurately to quarter degrees. 

It will be noticed that the letters E and W on the face of 
the compass are reversed from their true positions. These are 
so placed in order that when the sights are turned towards 
the west the north end of the needle will point towards the 
letter W, or if the sights are turned towards the east, the 
north end of the needle will point towards the letter E. It 
turns out that if the south sight standard is always turned 
towards the observer, the reading at the north end of the 
needle will indicate the true bearing of the line. Should the 
north sight standard be turned towards the observer, the read- 
ing at the south end of the needle would then be taken. 

Checking Bearings. When the bearing of a line has been 
taken, the instrument should be removed to the other end of 
the line and the reverse bearing taken. The number of 
degrees should be the same, but the letters should be reversed. 
Eor instance, if the direct bearing is N. 35§° W., the reverse 
bearing should be S. 35f° E. In case the reverse bearing is 
not what it ought to be, there is some mistake, or some local 
disturbance, or both. To detect errors a second trial at the 
direct bearing should be taken. To detect local disturbances 
take the direct and reverse bearings of other lines ranged out 
from the beginning of the line whose bearing is sought. If 
they all show the same difference between their two respective 
bearings, the evidence of some local disturbance, as iron, 



14 SURVEYING 

iron ore, etc., is pretty conclusive. In this case the true bear- 
ing of the line can be obtained by making the necessary cor- 
rection. In all cases, precautions should be taken to have the 
chain, pins, and other instruments that would affect the direc- 
tion of the needle sufficiently removed from the compass. 

Obstacles. When a fence or other obstruction interferes 
with placing the instrument over the line the instrument may 
be placed at one side, the ranging pole being correspondingly 
placed at the other end. If one end of the line cannot be seen 
from the other end, run a random line. Then (Fig. 6, p. 8) 
tan EL A = AE -s- LA, whence the angle EL A can be found. 
This angle combined with the bearing of the random line will 
give the bearing required. Or some point can be selected 
from which the ends of the line are visible. The distances to 
the ends may be measured, and the angle between the two 
auxiliary lines may also be measured: - Of the triangle thus 
formed, the angle at the beginning of the given line may be 
computed, and, when properly combined with the bearing of the 
first auxiliary line, will give the required bearing. If a single 
triangle is not sufficient, a series of triangles may be employed 
until the end of the line is reached. 

Measurement of Horizontal Angles. To measure a horizontal 
angle by means of the needle, place the compass over the 
vertex of the angle, take the bearing of each line separately, 
and combine these bearings according to the following rules, 
as suggested by Fig. 10 : 

1. If the first letters of the bearings are alike, and also the 
last letters, find the difference of the bearings. 

2. If the first letters are alike, and the last letters unlike, 
add the bearings. 

3. If the first letters are unlike, and the last also unlike, 
subtract the difference of. the bearings from 180°. 

4. If the first letters are unlike, and the last alike, subtract 
the sum of the bearings from 180°. 



FIELD INSTRUMENTS 



15 




Measurement of Vertical Angles. A vertical angle is an 
angle the sides of which are in a vertical plane. If one side 
of a vertical angle is horizontal and the other ascends, the 
angle is called an angle of elevation; if one side is horizontal 
and the other descends, the angle is called an angle of depres- 
sion. To measure an angle of elevation by means of the com- 
pass, sight through the lower eyepiece to a point that is as 
far above the point whose elevation is sought as the instru- 
ment is above the point from which the elevation is to be 
taken. Read off the degrees of the right-hand tangent scale, 
marked by a card placed squarely across the face of the south 
standard, the top of the card being in the line of sight. To 
measure an angle of depression, proceed in the same manner, 
using the upper eyepiece and the left-hand tangent scale. If 
the compass is provided with a telescopic sight that has a 
vertical circle attachment, these should be used instead of 
the eyepieces and tangent scales. 

Verniers. A vernier is a contrivance for measuring portions 
smaller than those into which a line is divided. We shall 
describe two kinds. 

Let AB (Fig. 11) be a portion of a line graduated to tenths 
and hundredths of a foot. VR is the vernier. 

In (a), nine parts of the line are divided into ten equal parts 
on the vernier. Hence, a division on the vernier is less than 
a division on the line by the difference between T i^ of a foot 
and ^o of T ^ of a foot, or T oV o °^ a f°°t- Now, if the vernier 



16 



SURVEYING 



is moved so that 1 of the vernier coincides with 1 of the scale, it 
has moved over a space equal to T J fT of a foot. If the vernier 
is moved so that 2 of the vernier coincides with 2 of the scale, 
it has moved over a space equal to tv %q of a foot ; and so on. 
In (5), 6 of the vernier coincides with 9 of the scale, which 
indicates that the zero of the vernier has moved past 3 of the 
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0.536 foot. This form of the vernier is known as the direct 
form, since the figuring, on the vernier proceeds in the same 
direction as that on the scale. 

In (c), eleven parts of the line are divided into ten equal parts 
on the vernier. Hence, a division on the vernier is greater 
than a division on the line by the difference between T ^ of 
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FIELD INSTRUMENTS 



17 



of the scale, i.e., the end of the 6th tenth, the vernier has 
moved over a space equal to j^q o °^ a foot- ^ the vernier is 
so moved that 2 of the vernier coincides with 9 of the scale, 
the vernier has moved over a space equal to t -£qq of a foot ; 
and so on. 

In (d), 6 of the vernier coincides with 7 of the scale, which in- 
dicates that the zero of the vernier has moved past 3 of the scale 
a space equal to T ^ f of a foot. The reading here is 0.636 foot. 
- This form of the vernier is known as the retrograde form, 
since the figuring on the vernier proceeds in the opposite direc- 
tion from that on the scale. In either form the following 
rule for using and reading the vernier may be adopted : 

Move the vernier tintil its zero line, or index, is at the point 
to which the required measurement is to be taken; read the 
main scale to the nearest division below the index, and that 
number of the division line of the vernier which stands opposite 
a line of the main scale. 




Fig. 12 



Compass Vernier and its Uses. Let LL' (Fig. 12) repre- 
sent the limb of the compass graduated to half degrees, and 
VV the vernier divided into thirty equal spaces, equal to 
twenty -nine spaces of the limb. Then, one space of the vernier 
is less than one space of the limb by l'(=30' — J^ of 29x30'), 
and the reading may be obtained to single minutes. 



18 



SURVEYING 



In Fig. 12 the index, or zero, of the vernier stands between 
32° and 32° 30', and the line of the vernier marked 9 coincides 
with a line of the limb. Hence, the reading is 32° 9'. 

When the index moves from the zero line of the limb in a 
direction opposite to that in which run the numbers of the 
limb, the number of minutes obtained as above must be sub- 
tracted from 30' to obtain the minutes required. (Why ?) If, 
however, the vernier is made double, that is, if it has thirty 
spaces on each side of the zero line, it is always read directly. 
The usual form of the double vernier, shown in Fig. 13, has 




Fig. 13 



only fifteen spaces on each side of the zero line. When the 
vernier is turned to the right less than 15' past a division line 
of the limb, read the lower figures on the left of the zero line 
at any coincidence ; if moved more than 15' past a division 
line of the limb, read the upper figures on the right of the 
zero line at any coincidence ; and vice versa. In this form of 
the double vernier it will be observed that the spaces on the 
vernier are larger than those on the limb, since the 30 equal 
spaces of the former are equal to 31 half-degree spaces of the 
latter. 



FIELD INSTRUMENTS 19 

The most important use of the vernier compass is in setting 
off the variation of the needle explained just below. If the 
variation of the needle at any place is known, by means of the 
vernier screw the compass circle may be turned through an arc 
equal to the variation. If the observer stands at the south 
end of the instrument, the vernier is turned to the right or left 
according as the variation is west or east. The compass now 
gives the bearings of the lines with the time meridian. 

In order to retrace the lines of an old survey, turn the 
sights in the direction of a known line and move the vernier 
until the needle indicates the old bearing. If no line is defi- 
nitely known, the change of variation from the time of the 
old survey will give the arc to be set off. 

Magnetic Declination. The magnetic declination, or varia- 
tion of the needle, at any place is the angle which the magnetic 
meridian makes with the true meridian, or north and south 
line. The variation is east or ivest, according as the north end 
of the needle lies east or west of the true meridian. Western 
variation is indicated by the sign +, and eastern by the sign — . 
The kinds of magnetic declination are put under three heads : 

1. Irregular variations, which are sudden deflections of 
the needle due to magnetic storms or other causes not well 
understood. 

2. Solar-diurnal variations, which in northern latitudes reach 
their farthest point east about 8 o'clock a.m., and their farthest 
point west about 2 o'clock p.m., varying from 5' in the winter 
in some localities to 20' in the summer in other localities. 

3. Secular variation, which is a change in the same direction 
for a period of years, then in the opposite direction for about 
the same time. 

It is not accurately known how long it takes a complete 
secular variation to run its course, but from data already 
obtained it seems probable that the period of time covered is 
not less than two and a half or three centuries. 



20 



SURVEYING 






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Charleston, S.C. . 
Pittsburg, Pa. . 

Erie, Pa 

Savannah, Ga. . . 
Cleveland, 0. . . 
Key West, Fla. 
Detroit, Mich. . . 
Sault Ste. Marie, Mich 
Cincinnati, 0. . 
Grand Haven, Mich. 
Nashville, Tenn. . 
Michigan City, Ind. 
Pensacola, Fla. . . 
Chicago, 111. . . . 
Milwaukee, Wis. . 
Mobile, Ala. . . 
New Orleans, La. . 
St. Louis, Mo. . . 
Duluth, Minn. . . 
Galveston, Tex. 
Omaha, Neb. . . . 
Austin, Tex. . . 
San Antonio, Tex. 
Denver, Col. 
Salt Lake City, Utah 
San Diego, Cal. 
Seattle, Wash. . . 
San Francisco, Cal. 
C. Mendocino, Cal. 



22 SURVEYING 

The agonic line, or line of no variation, is a line joining 
those places at which the magnetic meridian coincides with 
the true meridian. At the beginning of the present century 
this line crossed the United States in an irregular way from 
Michigan to South Carolina. It is gradually moving west- 
ward, so that the variation is increasing at places east of this 
line, and decreasing at places west of the line. East of this 
line the variation is westerly, and west of this line the varia- 
tion is easterly. Lines that join places of equal magnetic 
declination are called isogonic lines. 

Table of Magnetic Declination. On pp. 20, 21 will be found 
a table showing the variation in magnetic declination at 
different places in the United States and contiguous territory 
during the nineteenth century ; also the annual change for the 
epoch of 1900. 

EXERCISE H 

1. Lay out a field of five sides and take the bearings and 
measures of the sides in order, beginning at the most westerly 
point and going about the field clockwise. 

2. From the bearings obtained in Example 1 find the value 
of each of the interior angles. What is their sum ? 

3. Lay out the field the bearings and distances of whose 
sides are given in Example 1 of Exercise VI, p. 64. 

4. Eange out a line whose bearing is N. 38° 30' W., and at 
some point in this line range out another line making a right 
angle with it. What is the bearing of the second line ? 

5. Set up the compass at a spot near which there is known 
to be some local disturbance, as iron in a building, or an 
iron fence, and find the variation of the needle due to such 

disturbance. 



FIELD INSTKUMENTS 23 

SECTION V 
THE TRANSIT 

Surveyor's Transit. The transit is the most important 
instrument used in surveying. There are many modifications 
of it, each adapted to its own particular use. All, however, 
have about the same essential features. The one described 
here, and shown in Fig. 14, is the surveyor's transit, the one 
of most general use. The essential parts are the telescope 
with its axis and two standards, the circular plates with their 
attachments, the sockets upon which the plates revolve, the 
leveling head, and the tripod. Within the telescope are two 
fine cross wires, at right angles to each other, whose intersection 
determines the optical axis, or line of collimation, of the tele- 
scope. Under the telescope, and attached to it, is a spirit 
level by which horizontal lines may be run, or the difference 
of level between two stations be found. The axis of the tele- 
scope carries a vertical circle which measures vertical angles 
to single minutes by means of a vernier. The vernier plate, 
which carries the telescope and also the compass circle, has 
two verniers diametrically opposite to each other, and it moves 
entirely around the graduated limb of the main plate. The 
sockets are compound ; the interior spindle attached to the 
vernier plate turning in the exterior socket, when an angle is 
taken on the limb, but when the plates are clamped together 
the exterior socket itself, and with it the whole instrument, 
revolves in the socket of the leveling head. The transit is 
leveled by four leveling screws which pass through a plate 
firmly fastened to the ball spindle and rest in small sockets, 
these resting in turn on the upper side of the tripod plate. 
On the underside of this lower or tripod plate is an arrange- 
ment called a shifting centre, which enables the surveyor to 
change the position of the vertical axis horizontally without 



24 SURVEYING 

moving the tripod ; besides this there is, if specially ordered, 
a device called a quick-leveling attachment to bring the transit 
quickly to an approximately level position by the pressure of 
the hands after which the leveling screws are used. 

Uses. The transit may be used for all the purposes for 
which the compass may be used, but with much greater 
precision. The principal use, however, is in measuring hori- 
zontal angles by means of the graduated limb and verniers. 
It may be used, furthermore, in obtaining differences of level ; 
also, provided there is the attachment to the telescope known 
as the stadia, in measuring distances, especially over broken 
ground. A still further use, when the transit is supplied 
with what is known as a gradienter attachment, is in fixing 
grades as well as measuring distances. 

Getting the Transit Ready. The instrument should be set 
up so as to be firm, the tripod legs- being pressed into the 
ground until the plates are as nearly level as can conveniently 
be done by this means. For the subsequent leveling turn the 
instrument until the spirit levels on the vernier plate are 
parallel to the vertical planes passing through opposite pairs 
of the leveling screws. Take hold of opposite screw heads 
with the thumb and forefinger of each hand, and turn both 
thumbs in or out as is necessary to bring the bubble to its 
proper place, the left thumb always moving in the direction 
that the bubble is to move. For precise work, in addition to 
leveling by the leveling screws, it is advisable to level the 
plates by the telescope level, as this is much more sensitive 
than the levels on the plate. • In this operation the position 
of the level on the telescope must be observed over both sets 
of leveling screws, one half the correction being made by the 
axis tangent screw, the other half by the leveling screws. 
Before an observation is made with the telescope, the eye- 
piece should be focused by its pinion until the cross wires 
appear distinct ; the object glass is then focused by its pinion 



FIELD INSTRUMENTS 



25 




Fig. 14. The Surveyor's Transit 



26 SURVEYING 

until the object to be observed appears well defined. This 
latter process must be repeated when the distance to the 
object is changed. 

Measurement of Horizontal Angles. Place the instrument 
directly over the vertex of the angle, and level. Set the 
limb at zero by the tangent screw of the plates, and turn the 
telescope in the direction of one of the sides of the angle, 
directing it to the object by the tangent screw of the leveling 
head. Then unclamp the main plate and turn the telescope 
until it is in the direction' of the other side of the angle, 
and read the angle by the verniers. The object of the two 
verniers. on the vernier plate is to correct any mistakes that 
might arise from the want either of exact coincidence in the 
centres of the verniers and the limb or of exact graduations 
on the limb. The correct reading may be obtained by adding 
to the reading of one vernier the supplement of the reading of 
the other, and taking half their sum. 

Measurement of Vertical Angles. Direct the telescope to the 
object ; clamp, and read the angle indicated on the vertical 
circle by the vernier. The angle read will be an angle of 
elevation or depression as the case may be, the horizontal line 
being the line of collimation of the telescope when in a hori- 
zontal position. 

Stadia Measurements. As already stated on page 24, the 
stadia is an attachment to the telescope used in measuring 
distances, especially over rough ground. It consists essen- 
tially of two horizontal wires fastened to small movable 
slides, and so adjusted as. to include a given space, say 
one foot on a rod 100 feet distant. These wires will then 
include, two feet on a rod 200 feet away, or a half-foot at a 
distance of 50 feet, and so on. Usually the instrument is so 
adjusted that the zero of the indicated distance is in front 
of the centre of the instrument; hence, the true distance 
is the indicated distance plus the distance of this zero from 



FIELD INSTRUMENTS 27 

the centre of the instrument. This latter distance is deter- 
mined for each instrument by the maker, and noted on a card 
placed on the inside of the instrument box. It is known as 
the constant of the instrument. The readings are taken on a 
rod, specially designed for the purpose, known as the stadia 
rod. This is graduated to feet, and tenths and hundredths of 
a foot. Any ordinary leveling rod, if similarly graduated, will 
answer the same purpose. Obviously in taking stadia meas- 
urements the rod must always be held at right angles to 
the line of sight. This statement has special reference to 
measurements taken up or down hill-slopes. In this case, if 
horizontal distance is required, the measured distance must 
be multiplied by the cosine of the angle of elevation or 
depression. (Why ?) 



EXERCISE m 

1. By means of the transit, measure the interior angles of 
the field of Example 1, Exercise II, p. 22, and compare with 
the results obtained in Example 2 of the same exercise. 

2. Lay out the entire angular magnitude about some point 
into four or more angles, and measure each one of them. What 
should the sum of them equal ? 

3. If the constant of a transit adjusted to one foot 100 feet 
away is 3.8 inches, what is the true length of a line when the 
indication on the rod is 2.35 feet ? 

4. Measure a line by the stadia, and compare with measure- 
ments taken by the chain and also by the tape. 

5. Compute the height of a tall object, as a tree or steeple, 
by first measuring its distance from some convenient point and 
measuring the angle of elevation at that point. 

6. Lay out a square field containing just one acre. 



28 SURVEYING 

SECTION VI 
THE SOLAR COMPASS 

Description and Uses. A full description of the solar com- 
pass, or Burt's solar compass, as it is often called from its 
inventor, with its principles, adjustments and uses, forms the 
subject of a considerable volume, which should be in the hands 
of the surveyor who uses this instrument. The limits of our 
space will allow only a brief reference to its principal features. 
Fig. 15 exhibits the instrument by itself; Fig. 16, p. 31, is a 
graphical illustration of the solar apparatus as an attachment to 
the transit, the circles shown being intended to represent those 
supposed to be drawn upon the concave surface of the heavens. 
The form of the solar compass shown in Fig. 15 has the 
arrangement of its sockets and plates -similar to that of the 
transit, the standards similar to those of the compass, the solar 
apparatus being placed on the upper vernier plate and taking 
the place of the needle, for which it operates as a substitute 
in the field. 

The solar compass consists mainly of three arcs of circles, a 
the latitude arc, by which is set off the latitude of the place, b 
the declination arc, by which is set off the declination of the 
sun, and c the hour arc, by which is set off the hour of the day. 
The arm h is movable about a point at the extremity of the 
piece containing the declination arc, there being at each end a 
solar lens having its focus on a silvered plate on the other end. 
The arc of the declination limb turns on an axis, and one or 
the other solar lens is used, according as the sun is north or 
south of the equator. Fig. 15 shows the position of the decli- 
nation arc when the sun is south; Fig. 16, when it is north. 
The needle box is moved about its centre by a slow-motion 
screw. It contains a magnetic needle, and is furnished with a 
graduated arc about 36° in extent. 



FIELD INSTRUMENTS 



29 




Fig. 15. Burt's Solar Compass 



FIELD INSTRUMENTS 



31 




Fig. 16. Transit with Solak Attachment 

The circles shown in the cut are intended to represent in miniature circles supposed 
to be drawn upon the concave surface of the heavens. 



32 SURVEYING 

The solar compass may be used for most of the purposes of a 
compass or transit. Its most important use, however, is to run 
north and south lines, especially in laying out the public lands. 
It may be used also in determining the latitude of a place. 

To establish a True Meridian. Set off on the latitude arc 
the latitude of the place. Set off on the declination arc the 
declination of the sun, corrected for refraction. Set the 
instrument over the station ; level, and turn the sights in a 
north and south direction by the needle. The surveyor then 
turns the solar lens to the sun, and with one hand on the 
instrument and the other on the revolving arm, moves both 
from side to side until the sun's image is made to appear on 
the silvered plate, precisely between the equatorial lines. The 
line of sights then indicates the true meridian. 

The bearing of any line from the meridian may be read by 
the verniers of the horizontal limb. • ^When a due east and 
west line is to be run, these verniers are set at 90°, and the 
sun's image is kept between the lines as before. 

Other Methods. By North Star at Culmination. The North 
Star, or Polaris, at present revolves about the north pole of 
the heavens at the distance of about li° ; hence, it is on the 
meridian twice in 23 h. 56 m. 4 s. (a sidereal day), once above 
the pole, called the upper culmination, and 11 h. 58 m. 2 s. 
later below the pole, called the lower culmination. 

The time of the upper culmination of Polaris may be found 
by means of the star Mizar, the middle one of the three stars 
in the handle of the Dipper (in the constellation of the Great 
Bear). It crosses the meridian at nearly the same time as 
Polaris. Suspend a plumb line, placing the bob in a pail of 
water to lessen its vibrations. South of the plumb line, upon 
a horizontal board firmly supported, place a compass sight, or 
any upright with a small, opening or slit, fastened to a board 
a few inches square. At night, when Mizar by estimation 
approaches the meridian, place the compass sight in line with 



FIELD INSTRUMENTS 



33 



Cassiopeiae 



Polaris 



Polaris and the plumb line, and move it so as to keep it in 
this line until the plumb line falls also on Mizar (Fig. 17). 
Note the time ; then (1903) 3 m. 39 s. later Polaris will be 
on the meridian. If then Polaris, the plumb line and the com- 
pass sight are brought into line, the plumb line and compass 
sight will give two points in the meridian ; or if the telescope 
of the transit is brought to bear on Polaris, 
and a light is held near to make the wires 
visible if necessary, the telescope will 
then lie in the plane of the meridian, 
which may be marked by bringing the 
telescope to a horizontal position. 

For each year subsequent to 1903 add 
21 s. to 3 m. 39 s. If the lower culmina- 
tion takes place at night, the time may be 
found in a similar manner. When Mizar 
cannot conveniently be used, 8 Cassiopeiae 
(Fig. 17) may be employed, the method 
being the same as in the case of Mizar. 
The interval, however (1903), is 4 m. 24 s. 
and the annual increase of the interval '•■'■■ ■<■ 
about 20 s. 

By North Star at Greatest 'Elongation. 
When Polaris is at its greatest apparent 
angular distance east or west of the pole, 
it is said to be at greatest elongation. It 
attains its greatest eastern elongation and 
western elongation, respectively, 5 h. 59 m. 1 s. after lower and 
upper culmination. The azimuth of a star is the angle which 
the meridian plane makes with the vertical circle passing 
through the star and the zenith of the observer. 

If now we know the time of either extreme elongation and 
also the azimuth of Polaris at an extreme elongation, we can 
from these data establish a true meridian. The latter of these 



Pole 



Great 



Bear 



Fig. 17 



34 SURVEYING 

data is given for various latitudes and for years to come in 
tables, to which the surveyor is supposed to have access. To 
obtain a line in the direction of Polaris at greatest elongation, 
we may proceed as follows : A few minutes before the time 
of greatest elongation, place the compass sight in line with 
the plumb line and Polaris, keeping it in line with these until 
the star begins to recede. At this moment the sight and 
plumb line are in the required line. Or bring the telescope 
of the transit to bear on the star, and follow it keeping the 
vertical wire over the star until it begins to recede. The 
telescope will then be in the required line. In either case, 
after having the transit sighted in the direction of the line 
just found, turn it in the proper direction through an angle 
equal to the azimuth as found from the tables. 

The accompanying table * gives the Washington mean time 
of each tenth transit of Polaris (upper culmination) at the 
meridian of Washington, D.C. The last column contains the 
variation per day, to facilitate the interpolation of the time 
for any intermediate transit. 

The transit which occurs October 17 is the tenth transit 
following that which occurs on October 8. This is because 
two transits occur on October 13 ; the interval separating them 
being 23 h. 56 m. 4 s. of mean time. These two transits are 
introduced in the table for greater convenience, and as a safe- 
guard against error respecting the particular day of transits in 
that vicinity. The double lines merely call attention to the 
break thus caused in the series. 

By interpolation we may, by taking account of the longitude 
of any given station, find the local mean time of transit of 
Polaris at that station for any particular day. Thus, to find 
the Cincinnati mean time of the upper culmination of Polaris 
at Cincinnati, on May 15, 1902, we have (p. 36) : 

* Furnished by the Director of the Nautical Almanac Office, Wash- 
ington, D.C. 



FIELD INSTRUMENTS 



35 



Day of 


Local Mean Time 


Change in 


the Year 


of Every 10th Transit 


1 Day 


1902 


(Civil Time.) 




Jan. 1 


Qh 41m igs PM . 


- 3™ 56*.8 


11 


6 1 51 " 


56.9 


21 


5 22 22 " 


56.9 


31 


4 42 53 " 


56.9 


Feb. 10 


4 3 24 " 


56.8 


20 


3 23 56 " 


56.7 


Mar. 2 


2 44 29 " 


56.6 


12 


2 5 4" 


56.4 


22 


1 25 41 " 


56.2 


Apr. 1 


12 46 20 " 


56.0 


11 


12 7 1 " 


55.8 


21 


11 27 44 a.m. 


55.7 


May 1 


10 48 28 " 


55.7 


11 


10 9 14 " 


55.3 


21 


9 30 2 " 


55.1 


31 


8 50 51 " 


55.0 


June 10 


8 11 41 " 


55.0 


20 


7 32 31 " 


54.9 


30 


6 53 22 " 


54.9 


July 10 


6 14 13 " 


54.8 


20 


5 35 5 " 


54.9 


30 


4 55 56 " 


54.9 


Aug. 9 


4 16 47 " 


55.0 


19 


3 37 37 " 


55.1 


29 


2 58 26 " 


55.2 


Sept. 8 


2 19 14 " 


55.3 


18 


1 40 1 " 


55.4 


28 


1 46 " 


55.5 


Oct. 8 


12 21 30 " 


55.7 


Oct. 13 


12 1 51 A.M. 




Oct. 13 


11 57 55 p.m. 




Oct. 17 


11 42 12 p.m. 


55.8 


27 


11 2 53 " 


56.0 


Nov. 6 


10 23 32 " 


56.1 


16 


9 44 10 " 


56.3 


26 


9 4 46 " 


56.4 


Dec. 6 


8 25 21 " 


56.5 


16 


7 45 55 " 


56.7 


26 


7 6 27 " 


56.8 


36 


6 26 58 " 


- 3 56 .9 



36 SURVEYING 

Local mean time of transit at Washington, May 11, 1902 

= 10 h 9 m 14 s a.m. 
Longitude of Cincinnati ivest of Washington 

= + h 29 m 40 s = + d .021. 
May 15 d + d 021 = May 15 d 021. 
Preceding tabular date == May 11. 
Therefore, interval = 4 d .021. 

Daily variation = - 3 m 55 s . 3 = - 235 s . 3. 

Total change = 4.021 x (- 235 s .3) = - 15 m 46 s . 

10 h 9 m 14 s a.m. 
-15 46 
9 h 53 m 28 s a.m. 

Therefore, the required time is 9 h 53 m 28 s a.m., May 15, 1902. 



SECTION VII 
THE Y LEVEL 

Description. The essential parts of the Y level (Fig. 18) 
are, the telescope, which is of various lengths, usually about 
20 inches, and rests on supports called Y's, from their shape ; 
the spirit level, which is under the telescope and attached to 
it ; and the leveling head and tripod, which are similar to the 
same parts of the transit. 

Leveling Rod. There are several kinds of leveling rods, 
each possessing some merit peculiar to its purpose. The one 
shown in Fig. 19 is known as the Philadelphia leveling rod, 
and is the one in most common use. It is made of two pieces 
of wood, sliding upon each other, and held in position by a 
clamp. The front surface of each piece is graduated to hun- 
dredths of a foot up to 7 feet ; the back surface of the rear 
piece is figured from 7 to 13 feet, reading from the top down, 



FIELD INSTRUMENTS 



37 




Fig. 18. The Y Level 



38 



SURVEYING 



and it also has a scale by which the rod is read to half hun- 
dredths of a foot as it is extended. The target 
slides along the front of the rod and is held in 
place by two springs which press upon the sides 
of the rod. It has a square opening at the centre, 
through which the division line of the rod oppo- 
site to the horizontal line of the target may be 
seen. It also carries a scale by which heights 
may be read to half hundredths of a foot. For 
heights not greater than 7 feet, the target is 
moved up or down the front surface, the rod 
being closed and clamped; but when a greater 
height is required the target is fixed at 7 feet 
and the rear half of the rod extended to the 
required height. The rod thus becomes a self- 
reading rod 13 feet long* 

How to use Level and Rod. When the leveling 
instrument is used, the tripod should be set firm ; 
the spirit level should then be brought succes- 
sively over each opposite pair of leveling screws 
and leveled in each position, the operation being 
repeated until the bubble remains in the middle 
of the tube through an entire rotation of the tele- 
scope. Each time before taking an observation 
the instrument should be examined to see if it 
is still level. Care should be taken to bring the 
cross wires of the telescope precisely in focus and 
the object into such perfect view that the wires 
will appear, to be fastened to the surface, how- 
ever the eye is moved. For very accurate work 
the instrument should be shielded from the direct 
rays of the sun. 
FlG 19 The leveling rod should be held in a truly 

vertical position, the rodman standing squarely behind it. 



9i 



5i 



FIELD INSTRUMENTS 



39 



The target is then raised or lowered at the signal of the 
leveler until its horizontal line is cut by the intersection of 
the cross wires of the telescope. The reading is done by the 
leveler or the rodraan according to the kind of rod used. 

Substitutes for the Y Level. For ordinary work, the Sur- 
veyors or Engineer's Transit is often used. 

The plumb level (Fig. 20) consists of two pieces of wood 
joined at right angles. A straight line is drawn on the upright 
perpendicular to the upper edge of the crosshead. The instru- 
ment is fastened to a support by a screw through the centre of 
the crosshead. The upper edge of the crosshead is brought 
to a level by making the line on the upright coincide with a 
plumb line. 



— £ 



9 



Fig. 20 



Fig. 21 



Fig. 22 



A carpenters square can be made into a level by being 
supported by a post (Fig. 21), the top of which is split or sawed 
so as to receive the longer arm. The shorter arm is made 
vertical by a plumb line, which brings the longer arm to a 
level. 

The water level, as shown in Fig. 22, consists of two 
upright glass tubes cemented into a connecting tube of any 
material. The whole is nearly filled with water and sup- 
ported at a convenient height. The surface of the water 
in the uprights determines the level. The water should be 
colored. 



40 SURVEYING 

A level line may be obtained by sighting along the upper 
surface of the block in which an ordinary spirit level is 
mounted. 

For many purposes not requiring great accuracy, any of the 
foregoing simple instruments in connection with any graduated 
rod will be sufficient. 

EXERCISE IV 

1. Set up the level and take the readings on the leveling 
rod at two stations equally distant from the instrument. What 
does the difference of these readings indicate ? 

2. Set up the level successively at the two stations in 
Example 1, taking the readings on the leveling rod placed 
where the instrument was first. What does the difference of 
these readings indicate ? Ought this difference to be the 
same as that in Example 1? Explain. 

3. In the field of Example 1, Exercise II, p. 22, set up the 
level successively at the middle of each of the five sides, taking 
the readings on the rod each time at both adjacent stations of 
the field. Find the difference between the sum of the hind- 
sights and the sum of the foresights. What should this 
difference equal ? 



SECTION VIII 

THE PLANE TABLE 

Description and Uses. The plane table, an approved form of 
which is shown in Fig. 23, consists mainly of a drawing 
board made of well-seasoned wood, arranged in sections to pre- 
vent warping, and supported at a convenient height by a tripod 
and leveling head, with attachments for horizontal movement. 



FIELD INSTRUMENTS 



41 




Fig. 23. The Plane Table 



42 SURVEYING 

The board is provided with rollers or clamps or both, for 
keeping the paper secure and even. The plumbing arm has 
its end brought to a point which, however placed on the 
paper, is directly above the corresponding point on the ground 
determined by the plummet. The alidade is a ruler of brass 
or steel supporting a telescope with stadia or sight standards, 
whose line of sight is in or parallel to the same vertical plane 
with the beveled edge of the ruler. A compass with two 
spirit levels serves both to level the table and, when applied 
by the edges parallel to the zero line of the compass circle, 
to determine the magnetic bearing of the lines drawn on the 
paper, or the direction of the table itself. 

After the principal lines of a survey have been determined 
and plotted, the details of the plot may be filled in by means 
of the plane table ; or, when a plot only of a tract of land is 
desired and extreme accuracy is not required, this instrument 
affords the most expeditious means of obtaining it. There is 
little use for it outside of the United States Coast and Geodetic 
Survey and the United States Geological Survey. 

To orient the Table. This operation consists in placing the 
table so that the lines of the plot shall be parallel to the 
corresponding lines on the ground. 

This may be accomplished .approximately by turning the 
table until the needle of the compass indicates the same bear- 
ing as at a previous station, the edge of the compass coinciding 
with the same line on the paper at both stations. 

If, however, the line connecting the station at which the 
instrument is placed with another station is already plotted, 
the table may be placed in position accurately by placing it 
over the station so that the plotted line is by estimation over 
and in the direction of the line on the ground ; then making 
the edge of the ruler coincide with the plotted line, and turn- 
ing the board until the line of sight bisects the signal at the 
other end of the line on the ground. 



FIELD INSTRUMENTS 



43 




To plot any Point. Let ab on the paper represent the line 
AB on the ground; it is required to plot c, representing C on 
the ground. 

1. By intersection. 

Place the table in position at A (Fig. 24), plumbing a over A, and 
making the fiducial edge of the 
ruler pass through a ; turn the 
alidade about a until the line of 
sight bisects the signal at C, and 
draw a line along the fiducial edge 
of the ruler. Place the table in 
position at B, plumbing b over B, 
and repeat the operation just 
described. Then c is the intersec- 
tion of the two lines thus drawn. FlG ^ 

2. By resection. 

Place the table in position at A (Fig. 25), and draw a line in the direc- 
tion of C, as in the former case ; then remove the instrument to C, place 

it in position by the line drawn 
from a, make the edge of the 
ruler pass through b, and turn 
the alidade about b until B.is in 
the line of sight. A line drawn 
along the edge of the ruler will 
intersect the line from a in c. 

3. By radiation. 

Place the table in position at A 
(Fig. 26), and draw a line from a 
toward C, as in the former cases. 
Measure AC, and lay off ac to 
the same scale as ab. 

To plot a Field ABCD • • • 

By radiation. 

Set up the table at any point 
P, and mark p on the paper over 
P. Draw indefinite lines from p 




/ 


•> v 


1 
1 


\ 


1 


X 




b ^a 


B 



Fig. 25 




44 



SURVEYING 



toward A, B, C, ■ ■ ■ Measure PA, PB, • • • , and lay off pa, pb, 
suitable scale, and join a and b, b and c, c and d, ■ ■ ■ 



to a 





t» ^a 


B 



By progression. 

Set up the table at A, and draw 
a line from a toward B. Measure 
AB, and plot ab to a suitable 
scale. Set up the table in position 
at B, and in like manner deter- 
mine and plot be ; and so on. 



Fig. 27 



By intersection. 

Plot one side as a base line. 
Plot the other corners by the method of intersection, and join these points 
in proper order by straight lines. 

By resection. 

Plot one side as a base line. Plot the other corners by the method of 
resection, and join these points in proper order by straight lines. 

The Three-Point Problem. Let A, B, C represent three field 
stations plotted as a, b, c, respectively (Fig. 28) ; it is required 




fig. 2s 



to plot d representing a fourth field station D, from which A, 
B, and C are visible. 

Place the table over D, level and orient approximately by 
the compass. Determine d by resection as follows : Make the 



FIELD INSTRUMENTS 45 

edge of the ruler pass through a and lie in the direction a A, 
and draw a line along the edge of the ruler. In like manner, 
draw lines through b toward B and through c toward C. If 
the table is oriented perfectly, these lines meet at the required 
point d, but ordinarily they will form the triangle of error, ab, 
ac, be. In this case, through a, b, and ab ; a, c, and ac ; and 
b, e, and be, respectively, draw circles ; these circles will inter- 
sect in the required point d. For at the required point the 
sides ab, ac, be must subtend the same angle as at the points 
ab, ac, be, respectively. Hence, the required point d lies at 
the intersection of the three circles mentioned. The plane 
table may now be oriented accurately. 

The three-point problem may also be solved by fastening on the board 
a piece of tracing paper and marking the point d representing _D, after 
which lines are drawn from d toward A, B, and C. The tracing paper 
is then moved until the lines thus drawn pass through a, b, c, respectively, 
when by pricking through d the point is determined on the plot below. 
This method, however, is impracticable in case the wind blows. 



CHAPTER II 
OFFICE INSTRUMENTS 

SECTION IX 
PLOTTING INSTRUMENTS 

Definitions. A map is a representation by means of points, 
lines, and conventional signs on a plane surface, as on paper 
of a surveyed portion of the earth's surface, including objects 
upon it. If only the boundary lines- are drawn, the repre- 
sentation is called an outline map, or plot. The plot is a 
figure similar to the original, and the ratio of a line of the 
field to the corresponding line of the plot is called the scale. 
In surveying it is customary to designate the scale as so many 
chains to the inch. 

Principal Minor Instruments. The principal minor instru- 
ments used in plotting are a' ruler, pencil, straight-line pen, 
hair-spring dividers, compasses, a right triangle of wood or 
hard rubber, a T-square, and a parallel ruler. 

The Diagonal Scale. A portion of this scale is shown in 
Fig. 29. AB is the unit. AB and A'B' are divided into ten 
equal parts, and B is joined with h, the first division point to 
the left of B'; the first division point to the left of B is joined 
with the second to the left of B', and so on. The part of the 
horizontal line numbered 1 intercepted between BB' and Bh is 
evidently t l of J^ = T ^ of the unit ; the part of the hori- 
zontal line numbered 2 intercepted between BB' and Bh is T f „ 

of the unit, and so on. 

46 



OFFICE INSTRUMENTS 



47 



The method of using this scale is as follows : 
Let it be required to lay off the distance 1.43. 




Fig. 29 



Place one foot of the dividers at the intersection of the horizontal line 
numbered 3 and the diagonal numbered 4, and place the other foot at 
the intersection of the vertical line numbered 1 (CC) and the horizontal 
line numbered 3 ; the distance between the feet of the dividers will be 
the distance required. For, measuring along the horizontal line num- 
bered 3, from CC to BB' is 1 ; from BB' to Bh is 0.03 ; and from Bh to 
the diagonal numbered 4 is 0.4 ; and 1 + 0.03 + 0.4 = 1.43. 

The Circular Protractor. This instrument (Fig. 30) usually 
consists of a semicircular piece of brass or german silver, with 
its arc divided into degrees and its centre marked. 

Some protractors have an arm which carries a vernier, by 
which angles may be constructed to single minutes. Still 
others embrace an entire circle and have several arms with 
verniers. 

A rectangular protractor, having the degrees marked off on 
three sides of a plane scale, is sometimes used. Often this 
form of the protractor is found on the reverse side of the 
diagonal scale. 



48 



SURVEYING 



Constructions. 1. To lay off an angle with the circular 
protractor. Place the centre over the vertex of the angle, 
and make the diameter coincide with the given side of the 
angle. Mark off the number of degrees in the given angle, 
and draw a line through this point and the vertex. 




Fig. 30 

2. To draiv through a given point a line parallel to a given 
line with a right triangle and ruler. 

Make one of the sides of the triangle coincide with the 
given line, and, placing the ruler against one of the other sides, 
move the triangle along the ruler until the first side passes 
through the given point; then draw a line along this side. 

3. To draw through a given point a line perpendicular to 
a given line with a right triangle and ruler. 

Make the hypotenuse of the right triangle coincide with 
the given line, and' placing a ruler against one of the other 
sides of the triangle, revolve the triangle about the vertex of 
the right angle as a centre until its other perpendicular side 
is against the ruler ; then move the triangle along the ruler 
until the hypotenuse passes through the given point, and 
draw a line along the hypotenuse. 



OFFICE INSTRUMENTS 49 

SECTION X 
COMPUTING INSTRUMENTS 

The Planimeter. This is an instrument for measuring the 
area of any irregular field, by applying it to a plot of the 
field drawn accurately to scale. The form in most common 
use is that known as the polar planimeter. The essential 
parts are two arms, one fixed in length, the other adjustable, 
and a rolling wheel mounted on an axis parallel to the adjust- 
able arm. The outer end of the arm of fixed length is made 
fast to the plot by means of a needle point, and the free end 
of the other arm is made to trace the perimeter of the figure 
to be measured. A disk records the area in the unit for 
which the instrument is set. 

The Slide Rule. This is an instrument for effecting the 
processes of multiplication, division, involution, and evolution 
by means of logarithms. It consists of a series of scales so 
arranged that by sliding one upon the other the addition or 
subtraction of logarithms is mechanically performed. For a 
full description of this labor-saving device in its various forms, 
the student is referred to some treatise on the subject. 



CHAPTER III 

LAND SURVEYING 

SECTION XI 

DEFINITIONS 

Land Surveying is the art of measuring, laying out, and 
dividing land, computing parts and areas from measured parts, 
and preparing a plot. An original survey includes laying out 
the boundary lines and establishing the corners. A resurvey 
is the retracing of old boundary lines -and the finding of corner 
monuments, or the relocating of them when lost. 
Rules for Areas. The unit of land measure is the 

acre = 10 square chains = 4 roods 

= 160 square rods, perches, or poles. 
Areas are referred to the horizontal plane, no allowance 
being made for inequalities of surface. 

Let A, B, and C be the angles of a triangle, and a, b, and 
c the opposite sides, respectively, and let s = %(a + b + c). 
Area of triangle ABC = \ base x altitude 
= ^ be sin A 

a 2 sin B sin C 
~ 2 sin (B + C) 



= y/s (s — a)(s — b) (s — c). 
Area of rectangle = base x altitude. 
Area of trapezoid = ^ sum of parallel sides x altitude. 

Note. Spanish American units are in use in Texas, California, and 
Mexico. In this system the vara is the unit of length, which in Texas is 

50 



LAND SURVEYING 51 

reckoned 33£ inches, in California 33 inches, in Mexico 32.9927 inches. 
The area of a square 1000 varas on a side is called a labor, and of a 
square 5000 varas on a side is called a league. 



SECTION XII 
SPECIAL METHODS OF SURVEYING, AND COMPUTING AREAS 

Triangular Fields. Measure, as may be most convenient, 
the three sides, two sides and the included angle, two angles 
and the included side, or a side and the altitude upon that 
side, and compute the area by the appropriate formula. 

Fields having More than Three Straight Sides. Divide the 
field into triangles and take the sum of the areas of the 
triangles. Or, run a diagonal and perpendiculars to it from 
the opposite vertices ; take the sum of the areas of the right 
triangles, rectangles, and trapezoids thus formed. 

A third method is as follows : Let ABCD (Fig. 31) repre- 
sent a field, and P and P' two stations within it. (They may 
be without the field.) Measure D 
PP' with great exactness. Meas- 
ure the angles • between PP' and 
the lines from P and P' to the 
corners of the field. 

In the triangle P'PD, PP' and 
the angles PP'D and P'PD are 
known ; hence, PD may be found. 
In like manner, PC may be found. 
Then, in the triangle PDC, PD, 
PC, and the angle DPC are known ; hence, the area of PDC 
may be computed. In like manner, the areas of all the trian- 
gles about P or P' may be determined. 

Area ABCD = PAD + PDC + PCB + PBA; 
also, area ABCD = P'AD + P'DC + P'CB + P'BA. 




52 



SURVEYING 



Fields having Irregular Boundary Lines. Let A GBCD (Fig. 32) 
represent a field having a stream AEFGHKB as a boundary 
line. Run the line AB. From E, F, G, H, K, prominent 
points on the bank of the stream, let fall perpendiculars EE', 
FF', GG', etc., upon AB. Regarding AE, EF, etc., as straight 





Fig. 32 



Fig. 33 



lines, the portion of the field cut off by AB is divided into 
right triangles, rectangles, and trapezoids, the necessary ele- 
ments of which can be measured and the areas computed. 
The sum of these areas added to the area of ABCD gives 
the area required. If the offsets are at regular intervals, then 
the area of the part cut off by AB may be found by adding the 
offsets and multiplying by the common distance between them. 

When the irregular boundary line crosses the straight line 
that joins its extremities, as in Fig. 33, the areas of AEFH and 
HGB may be found separately, as in the preceding case. Then, 
the area required = ABCD + HGB — AEFH. 

Rectangular System of Co-ordinates. Let XX' and YY' (Fig. 
34) be two fixed perpendicular lines intersecting at the point O. 
Let the four parts into which these lines divide the plane be 
called Quadrants, as in Trigonometry, and be distinguished by 
naming them, respectively, first, second, third, and fourth 
quadrants. 

Suppose the position of a point is described by saying that 
its distance from YY', expressed in terms of some chosen unit 



LAND SURVEYING 



53 



II 



N 



III 



?-F 



IV 



M 



-II 



Y 
Fig. 34 



of length, is 3, and its distance from XX' is 4. Then there 
is in each quadrant one point and only one which will 
satisfy these conditions. The position of the point in each 
quadrant may be found by drawing parallels to YY' at the 
distance 3 from YY', and parallels 
to XX' at the distance 4 from XX' ; E~ 
then the intersections P v P 2 , P 3 , 
and P 4 satisfy the given condi- 
tions. X rrt k !-- X 

In order to determine which 
one of the four points, Pi, P 2 , P s , 
P 4 , is meant, we adopt the rule G- 
that distances measured from YY' 
to the right are positive; to the 
left, negative. Distances measured from XX' upward are 
positive ; downward, negative. Then, the position of P 1 will 
be denoted by + 3, + 4 ; of P 2 , by - 3, + 4 ; of P 3 , by — 3, - 4; 
of P 4 , by + 3, - 4. 

The fixed lines XX' and YY' are called the Axes of Co-ordi- 
nates ; XX' is called the Axis of Abscissas, or Axis of x ; YY', 
the Axis of Ordinates, or Axis of y. The intersection is 
called the Origin. 

The two distances (with signs prefixed) which determine 
the position of a point are called the Co-ordinates of the 
point ; the distance of the point from YY' is called its 
Abscissa ; and the distance from XX', its Ordinate. 

Abscissas are usually denoted by x, and ordinates by y, 
and a point is represented algebraically by simply writing 
the values of its co-ordinates within parentheses, that of the 
abscissa being always written first. 

Thus, P x (Fig. 34) is the point (3, 4), P 2 the point 
(— 3, 4), P, the point (— 3, — 4), and P 4 the point (3, — 4). 
In general the point whose co-ordinates are x and y is the 
point (x, y). 



54 



SURVEYING 



This system of co-ordinates may be applied to the determi- 
nation of areas in the following manner : 

Suppose the field to be ABODE (Fig. 35). Lay out the two 
axes so that the field shall lie wholly within the first quad- 
rant. Then measure the co-ordinates of each of the vertices 




and designate them as follows : for A, (x 1} yd ; for B, (x 2 , y 2 ) ; 
for C, (x 3 , y 3 ) ; for D, (x±, y 4 ) ; for E, (x 5 , yd- Evidently each 
of these co-ordinates is positive. Then, 

area ABODE = area LABM + area MBCP + area PCDR 

— area NEDR — area LA EN; 

or, in terms of the co-ordinates, 

area ABODE = %(y x + yd (x % — x x ) + \ (y 2 + y s ) (x 3 — x 2 ) 

+ £ (y» + yd ( x i - » 8 ) - iO'+ yd («4 - *s) 

= h\ x i (ys — yd + x* (yi - yd + * 3 (y* - yd 

+ %i (y s - yd + * 5 (>4 -yd\- 

This method can be put in the form of a general rule : 
Take one-half the algebraic sum of the products obtained 
by multiplying the abscissa of each vertex by the difference 
between the ordinates of the two adjacent vertices, taken in 
the clockwise order. 



LAND SURVEYING 



55 



EXERCISE V 

1. Required the area of a triangular field whose sides are 
13 chains, 14 chains, and 15 chains. 

2. Required the area of a triangular field if it has two 
angles 48° 30' and 71° 45', and the included side 20 chains. 

3. Required the area of a triangular field whose base is 
12..60 chains, and altitude 6.40 chains. 

4. Required the area of a triangular field which has two sides 
4.50 chains and 3.70 chains, and the included angle 60°. 

5. Required the area of a field in the form of a trapezium, 
one of whose diagonals is 9 chains, and the two perpendicu- 
lars upon this diagonal from the oppo- 
site vertices 4.50 chains and 3.25 chains. 

6. Required the area of the field 
ABCDEF (Fig. 36), if 
A E = 9.25 chains, FF' = 6.40 chains, 
BE = 13.75 chains, DD' = 7 chains, 
-DB = 10 chains, CC = 4 chains, 

and A A' = 4.75 chains. fig. 36 

7. Determine the area of the field ABCD from two interior 
stations P and P', if PP' = 1.50 chains, 




PP'C= 89° 35', 



PP'D = 349° 45', 
P'PB = 3° 35', 
P'PA = 113° 45', 



PP'B = 185° 30', 
PP'A = 309° 15', 

8. Required the area of the field 
ABCDEF (Fig. 37), if 
AF' = 4 chains, FF' = 6 chains, A 
EE' = 6.50 chains, AE' = 9 chains, 
AD = 14 chains, AC" = 10 chains, 
AB' = 6.50 chains, BB' = 7 chains, 
CC = 6.75 chains. 



P'PD = 165° 40', 
P'PC = 303° 15'. 




56 SURVEYING 

9. Kequired the area of the field AGBCD (Fig. 32, p. 52), 
if the diagonal A C = 5, BB' (the perpendicular from B to AC) 
= 1, DD' (the perpendicular from D to A C) = 1.60, EE' = 
0.25, PP' = 0.25, GG> = 0.60, ##' = 0.52, KK'= 0.54, .4P' = 
0.2, E'F' = 0.50, F'G' = 0.45, £'#' = 0.45, H'K' = 0.60, and 
K'B = 0.40. 

10. Eequired the area of the field AGBCD (Fig. 33, p. 52), 
if AD = 3, AC '= 5, .45 = 6, angle £U C = 45°, angle BA C = 
30°, J1.E' = 0.75, AF' = 2.25, AH = 2.53, .1G-" = 3.15, EE' = 
0.60, FF' = 0.40, and GG' = 0.75. 

11. Determine the area of the field A BCD from two exterior 
stations P and P', if PP' = 1.50 chains, 

P'PB = 41° 10', P'PP = 104° 45', PP'B = 132° 15', 
P'p.4 = 55° 45', PP'D = 66° 45', +PP'A = 103° 0'. 
p'PC = 77° 20', PP'C = 95° 40', 

12. Find the area of the field ABCDE (Fig. 35, p. 54), if 
the co-ordinates, in chains, of the vertices taken in order are 
(1.40, 6.75), (4.60, 8.32), (9.00, 9.05), (12.15, 5.58), and 
(5.27, 1.16). 

13. Find the area of the field ABCDE (Fig. 35, p. 54), by 
measuring distances as follows : 

AL = 400 feet ; BM = 700 feet ; CP = 680 feet ; 
DR = 380 feet ; EN = 200 feet; LM = 150 feet ; 
MN = 250 feet; NP = 200 feet ; PR = 220 feet. 

14. Lay out a field of four sides, and find its area by the 
method of triangles and also by the method of rectangular 
co-ordinates. 

15. Lay out a field of six sides, and find its area by the 
method of triangles and also by the method of rectangular 
co-ordinates. 



LAND SURVEYING 57 

SECTION XIII 
GENERAL METHOD FOR FARM SURVEYS 

Definitions. A course is the bearing and length of a 
line. The latitude of a course is the distance between the 
parallels through its extremities, and is called a northing or a 
southing, as the course is northward or southward. The 
departure of a course is the distance between the meridians 
through its extremities, and is' called an easting or a westing, 
as the course is eastward or westward. The meridian dis- 
tance of a point is its distance from a meridian. The double 
meridian distance of a course is double the meridian distance of 
its mid-point, and therefore equal to the sum of the meridian 

distances of the extremities of the 

M 
course. 

Let AB (Fig. 38) represent a line, 
whose bearing and length are known. 
Let MN be a reference meridian ; 
and let j) and^' be parallels through 
A and B, and m and m' meridians 
through the same points. Then, N 
angle mAB represents the bearing FlG " 38 

of line AB. The latitude of the course AB is AE, and its 
departure EB. The meridian distance of the point B is BC 
and of A, AD. Evidently, the double meridian distance of 
the course AB is ±(BC + AD). 

Again, in the triangle AEB, 

A E = AB x cos EAB, and EB = AB x sin EAB. 
Hence, latitude = distance x cos of bearing, and departure = 
distance x sin of bearing. From these formulas, the latitude 
and departure of any course may be found by means of a 
table of natural sines and cosines. They may be found also 



58 



SURVEYING 



from the Traverse Table, which is merely the tabulated results 
of the foregoing method for given courses. 

Field Notes. The field notes are kept in a book provided 
for the purpose. The page is commonly ruled in three col- 
umns, in the first of which is written the number of the 
station ; in the second, the bearing of the side ; and in the 
third, the length of the side. 

Field Notes 

N 




1 


N. 20° E. 


8.66 


2 


S. 70° E. 


5.00 


3 


S. 10° E. 


10.00 


4 


N. 70° W. 


10.00 



Fig. 39 



To obtain the field notes, say of field 
ABCD (Fig. .30), place the compass 
at A, the first station, and take the 
bearing of AB (p. 12) ; suppose it to 
be N. 20° E. Write the result in 
'D the^cond column of the field notes 
opposite the number of the station. 
Measure AB = 8.66 chains, and write 
the result in the third column of the 
field notes. Place the compass at B, 
and, after testing the bearing of A B (p. 13), take the bear- 
ing of BC, measure BC, and write the results in the field 
notes ; and so continue until the bearing and length of each 
side have been recorded. 

Computation of the Area. The survey may begin at any 
corner of the field ; but, for computing the area, the field notes 
should be arranged so that the most eastern or the most western 
station shall stand first. For the sake of uniformity, we shall 
always begin with the most western station and keep the field 
on the right in passing around it. 



LAND SURVEYING 



59 



The field notes occupy the first three of the eleven columns in the tablet 
below. Columns IV, V, VI, and VII contain the latitudes and departures 
corresponding to the sides, taken from the Traverse Table. The line 
represented by each number is indicated immediately above that number. 
Column VIII contains the meridian distances of the points B, C, D, and 
A, taken in order. Column IX contains the double meridian distances 



I 


II 


HI 


IV 


V 


VI 


VII 


VIII 


IX 


X 


XI 


Side 


Beaking 


DlST. 


N, 


S. 


E. 


W. 


M.B. 


B.M.D.. 


N.A. 


S.A. 


AB 
BC 
CD 
DA 


N.20°E. 
S.70°E. 
S. 10° E. 
N.70°"W. 


8.66 
5.00 
10.00 
10.00 


AB 1 
8.14 

D'A 
3.42 


B'C 
1.71 
CD' 
9.85 


BB' 
2.96 
C"C 
4.70 
D'D 
1.74 


DD' 

9.40 


BB' 
2.96 
CC 
7.66 
DD' 
9.40 




BB' 

2.96 
BB' + CC 

10.62 
CC'+DD' 

17.06 

DD' 

9.40 


2 ABB' 
24.0944 

2 ADD' 
32.1480 


2 C'CBB' 
18.1602 

2 D'DCC 
168.0410 






33.66 


11.56 


11.56 


9.40 


9.40 






56.2424 


186.2012 



(186.2012 sq. ch. - 56.2424 sq. ch.) + 2 = 64.98 sq. ch. = 6.50 acres. 

of the courses. Their composition is indicated by the letters immedi- 
ately above the numbers. Column X contains the products of the double 
meridian distances by the northings in the same line. The first number, 
24.0944 = 2.96 x 8.14 = BB' x AB' = twice area of triangle ABB' ; 
"32.1480 = 9.40 x 3.42 = DD' x AD' = twice area of triangle ABB'. 
Column XI contains the products of the double meridian distances by 
the southings in the same line. The first number, 

18.1602 = 10.62 x 1.71 = (BB' +-CC) x B'C 

— twice area of trapezoid C'CBB' ; 
168.0410 = 17.06 x 9.85 = (CC + DD') x D'C" 

= twice area of trapezoid D'DCC. 
The sum of the north areas in column X 

= 56.2424 = 2 (ABB' + ADD'). 
The sum of the south areas in column XI 

= 186.2012 = 2 (C'CBB' + D'DCC). 
But (C'CBB' + D'DCC) - (ABB' + ADD') = ABCD. 

Hence, 2 (C'CBB' + D'DCC) - 2 (ABB' + ADD') = 2 ABCD ; 
that is, 186.2012 - 56.2424 = 129.9588 = 2 ABCD. 

Hence, area ABCD = i of 129.9588 sq. ch. = 64.98 sq. ch. = 6.50 A. 



60 SURVEYING 

Balancing the Work. In the survey, we pass entirely around 
the field ; hence, we move just as far north as south. There- 
fore, the sum of the northings should equal the sum of the 
southings. In like manner, the sum of the eastings should 
equal the sum of the westings. In this way the accuracy of 
the field work may be tested. 

In the example on page 59 the sum of the northings is 
equal to the sum of the southings, being 11.56 in each case ; and 
the sum of the eastings is equal to the sum of the westings, 
being 9.40 in each case. Hence, the work balances. 

In actual practice the work seldom balances. When it 
does not balance, corrections are generally applied to the 
latitudes and departures by the following rules : 

1. The perimeter of a field is to any one side as the total 
error in latitude is to the correction required. 

2. The perimeter of a field is to any one side as the total 
error in departure is to the correction require'd. 

Example. The perimeter of a field measured 306.62 chains 
and one side 72.47 chains, with a total error of 22 links in 
latitude and of 18 links in departure. 

Then 306.62 : 72.47 = 22 links : x = 18 links : y. 

Whence x = 5 links and y = 4 links. 

Hence the correction in latitude applied to the given side is 
0.05 chains, and the correction in departure is 0.04 chains. 

If special difficulty was found in taking a particular bear- 
ing, or in measuring a particular line, the corrections should 
be applied to the corresponding latitudes and departures. 

The amount of error allowable varies in the practice of dif- 
ferent surveyors, and according to the nature of the ground. 
An error of 1 link in 8 chains would not be considered too great 
on smooth, level ground ; while on rough ground an error of 
1 link in 3 chains might "be allowed. If the error is consider- 
able, the field measurements should be repeated. 



LAND SURVEYING 



61 



As another example let it be required to find the area of 
field ABCDEF from the following 

Field Notes 



1 


N. 73° 30' W. 


5.00 


2 


S. 16° 30' W. 


5.00 


3 


N. 28° 30' W. 


7.07 


4 


N. 20° 00' E. 


11.18 


5 


S. 43° 30' E. 


5.00 


6 


S. 13°30'E. 


10.00 



Side 


Bearing 


DlST. 


N. 


S. 


E. 


W. 


M.D. 


D.M.D. 


N.A. 


S.A. 


AB 
BC 
CD 
DE 
EF 
FA 


N.20°00'E. 
S.43°30'E. 
S.13°30'E. 
N. 73°30"W. 
S.16°30"W. 
N. 28° 30'W. 


11.18 
5.00 

10.00 
5.00 
5.00 
7:07 


10.51 

1.42 
6.21 


3.63 

9.72 

4.79 


3.82 
3.44 
2.33 


4.79 
4.80 
1.42 

3.37 


BB 

3.82 

C'C 
7.26 
DD 
9.59 

E'E 
4.79 
F'F 
3.37 

0.00 


BB 
3.82 

B'B+C'C 
11.08 

CC + D'D 

16.85 
DD + E'E 

14.38 
E'E + F'F 

8.16 

F'F 

3.37 


2 ABB' 
40.1482 

2 D'DEE' 
20.4196 

2AFF' 
20.9277 


2 C'CBB' 
40.2204 

ID'DCC 
163.7820 

2 F'FEE' 
39.0864 






43.25 


18.14 


18.14 


9.59 


9.58 
9.59 






81.4955 


243.0888 



43.25 : 5 = 0.01 : x. 



Area = 8.08 acres. 



The first station in the field notes is D, but we rearrange the numbers 
in the tablet so that A stands first. The northings and southings balance, 
but the eastings exceed the westings by 1 link. We apply the correction 
to the westing 4.79 (the distance DE being in doubt), making it 4.80, and 
write the correction. In practice, the corrected numbers are written in 
red ink, and often all the latitudes and departures are rewritten in four 
additional columns, headed, respectively, N', S', E', W. 

Supplying Omissions. If for any reason the bearing and the 
length of any side do not appear in the field notes, the lati- 
tude and departure of this side may be found in the following ' 
manner : 



62 



SURVEYING 



Find the latitudes and departures of the other sides as 
usual. The difference between the northings and southings 
gives the northing or southing of the unknown side, and the 
difference between the eastings and westings gives the easting 
or westing of the unknown side. 

If the length and the bearing of the unknown side are de- 
sired, they may be found by solving the right triangle, whose 
sides are the latitude and departure found by the method just 
explained, and whose hypotenuse is the length required. 

Obstructions. If the end of a line is not visible from 
its beginning, or if the line is inaccessible, its length and 
bearing may be found as follows : 

By means of a random line (p. 8). 

When it is impossible to run a random line, which is fre- 
quently the case on account of the extent of the obstruction, 
the following method may be used : 

Let AB (Fig. 40) represent an inaccessible line 
whose extremities A and B only are known, and B 
invisible from A. 

Set flagstaffs at convenient points, C and D. 
Find the bearings and lengths of AC, CD, and DB, 
and then proceed to find the latitude and departure 
of AB. 




Fig. 40 



Example. 

lowing notes (see Fig. 40) : 



Suppose that we have the fol- 



Side 


Bearing 


DlST. 


N. 


s. 


E. 


w. 


AC 
CD 
BB 


S. 45° E. 

E. 

N. 30° E. 


3.00 

3.50 
4.83 


4.18 


2.12 


2.12 
3.50 
2.42 




,- 


4.18 


2.12 


8.04 






LAND SURVEYING 



63 



The northing of AB is AE = 2.06, and the easting, EB = 8.04. These 
numbers may be entered in the tablet ha the columns N. and E., opposite 
the side AB. 

If the bearing and length of AB are required, 

. „.„ BE 8.04 

tan BAE = = 

AE 2.06 

Hence, the angle BAE = 75° 38'. 
Also, 



5.903. 



AB = ~^AE 2 + BE 2 = V8.04 2 + 2.06 2 = 8.30. 
Therefore, the bearing and length of AB are N. 75° 38' E. and 8.30. 

To make a Plot. A plot or map may be drawn to any 
desired scale. If a line 1 inch in length in the plot represents 
a line 1 chain in length, the plot is 
said to be drawn to a scale of 1 chain 
to an inch. In this case (Fig. 41) the 
plot is drawn to a scale of 8 chains 
to an inch. 

Draw the line NAS to represent 
the meridian, and lay off the first 
northing AB' = 8.14. Through B 
draw an indefinite line perpendicular 
"to NS and lay off B'B, the first easting, 
= 2.96. Draw AB ; then the line AB 
represents the first side of the field. 
Through B draw BC" perpendicular 
to BB', and make BC" = 1.71, the first 
southing. Through C" draw C"C 
perpendicular to BC", and equal to 
4.70, the second easting. Draw BC. 
The line BC represents the second 
side of the field. Proceed in like 
manner until the field is completely 
represented. The extremity of the 
last line F'A, measured from F', should fall at A. 
test of the accuracy of the plot. 




Fig. 41 



This is a 



64 



SURVEYING 



By drawing AC, AE, and EC, the hexagonal figure 
ABCDEFA is divided into triangles, the bases and altitudes 
of which may be measured and the area computed approxi- 
mately. 

Another method is as follows : 
Draw MN (Fig. 42) to represent a 
meridian. Let the' point A in this 
line be taken as the first station in 
the rearranged field notes of page 
61. With the circular protractor 
mark off each of the bearings as b, c, 
d, e, f, and a. Draw AB to scale 
through b. With triangle and ruler 
(p. 48) or with parallel ruler draw to 
scale BC parallel to Ac ; and so on. 

After some * practice, still other 
methods will be suggested, but the 

methods given are among the best. 
Fig. 42 & & 




EXERCISE VI 

Find the areas of the following and make a plot of each. 
In 3 and 7, detours were made on account of obstructions 
(p. 62). The notes of the detours are written in braces. 

12 3 



St a. 


Bearings 


DlST. 


1 


S. 75° E. 


6.00 


2 


S. 15° E. 


4.00 


3 


S. 75° W. 


6.93 


4 


N. 45° E. 


5.00 


5 


N. 45° W. 


5.19* 



Sta. 


Bearings 


DlST. 


1. 

2 
3 
4 


N. 45° E. 
S. 75° E. 
S. 15° W. 
N. 45° W. 


10.00 
11.55 
18.21 
19.11 



Sta. 


Bearings 


DlST. 


1 


S. 2°15'E. 


9.68 


2J 


N. 51°45'W. 


2.39 


S. 85°00'W. 


6.47 


1 


S. 55°10'W. 


1.62 


3 


N. 3°45'E. 


6.39 


4 


S. 66°45'E. 


1.70 


5 


N. 15°00'E. 


4.98 


6 


S. 82°45'E. 


6.03 



LAND SURVEYING 



65 



STA. 


Bearings 


DlST. 


1 


N. 6°30'W. 


6.08 


2 


S. 82°30'W. 


6.51 


3 


S. 3°00'E. 


5.33 


4 


E. 


6.72 



Sta. 


Bearings 


DlST. 


1 
2 
3 
4 


N. 6°15'W. 
S. 81°50'W. 
S. 5°00'E. 
N. 88°30'E. 


6.31 
4.06 
5.86 
4.12 



Sta. 


Bearings 


DlST. 


1 


N. 20°00'E. 


4.621 


2 


N. 73WE. 


4.16* 


3 


S. 45°15'E. 


6.18* 


4 


S. 38°30'W. 


8.00 


5 


Wanting 


Wanting 



Sta. 


Bearings 


DlST. 


'{ 


S. 81°20'W. 


4.28 


N. 76°30'W. 


2.67 


2 


N. 5°00'E. 


8.68 


3 


S. 87°30'E. 


5.54 


r 


S. 7°00'E. 


1.79 


4 


S. 27°00'E. 


1.94 


S. 10°30'E. 


5.35 


i 


N. 76°45'W. 


1.70 



Sta. 


Bearings 


DlST. 


1 


K 89°45'E. 


4.94 


2 


S. 7°00'W. 


2.30 


3 


S. 28°00'E. 


1.52 


4 


S. 0°45'E. 


2.57 


5 


N. 84°45'W. 


5.11 


6 


N. 2°30'W. 


5.79 



9. An Ohio farm is bounded and described as follows : 
Beginning at the southwest corner of lot No. 13, thence N. 1£° 
E. 132 rods and 23 links to a stake in the west boundary 
line of said lot ; thence S. 89° E. 32 rods, and 15 t 4 q links to 
a stake; thence N. li° E. 29 rods and 15 links to a stake 
in the north boundary line of said lot ; thence S. 89° E. 61 
rods and 18 t 6 q links to a stake; thence S. 32^-° W. 54 rods 
to a stake ; thence S. 35^° E. 22 rods and 4 links to a 
stake ; thence S. 48° E. 33 rods and 2 links to a stake ; 
thence S. 7^° W. 76 rods and 20 links to a stake in the south 
boundary line of said lot ; thence N. 89° W. 96 rods and 10 
links to the place of beginning. Containing 85.87 acres, more 
or less. 

Verify the area given and plot the farm. 



66 SURVEYING 

Modification of the Latitude and Departure Method. The area 
of a field may be found by a modification of the latitude and 
departure method, if its sides and interior angles are known. 

Let A, B, C, D represent the interior angles of the field 
ABCD (Fig. 43). Let the side AB determine the direction of 
reference. The bearing of AB, with reference to AB, is 0°. 
The bearing of BC, with reference to. AB, is the angle 
b = 180° — B. The bearing of CD, with reference to AB, is 
the angle c = C — b. The bearing of DA, with reference 

to AB, is the angle d = A. 

The area may now be com- 
puted by the latitude and depar- 
ture method, regarding AB as the 
meridian. 

In practice, the exterior angles, 
when acut^e, are usually measured. 
As the interior, angles may be 
measured with considerable accu- 
racy by the transit, the latitudes 
and departures should be obtained by using a table of natural 
sines and cosines. 

EXERCISE VII 

1. Find the area of the field ABCD, in which the angle 
A = 120°, B = 60°, C = 150°, and D = 30° ; and the side 
AB = 4 chains, BC = 4 chains, CD = 6.928 chains, and DA = 
8 chains. 

Keep three decimal places, and use the Traverse Table. 

2. Find the area of the farm ABCDE, in which the angle 
A = 106° 19', B = 99° 40', C = 120° 20', D = 86° 8', and E = 
127° 33'; and the side ,45 = 79.86 rods, BC = 121.13 rods, 
CD = 90 rods, DE = 100.65 rods, and EA = 100 rods. 

Use the table of natural sines and cosines, keeping two decimal places 
in the results. 




LAND SURVEYING 67 

General Remarks on determining Areas. Operations depend- 
ing upon the reading of the magnetic needle must lack 
accuracy. Hence, when great accuracy is required (which is 
seldom the case in land surveying) the method of pp. 58-61 
cannot be employed. 

The best results are obtained by the methods explained on 
pp. 51-54 and 66, the horizontal angles being measured with 
the transit, and great care exercised in measuring the lines. 



SECTION XIV 
LOCATION SURVEYS 

Definition. In surveying proper we measure lines and 
angles as we find them, while in location surveys we mark them 
out on the ground where they are required to be in order to 
inclose a given area, or conform to a specified shape, or meet 
some other given condition. Laying out, parting off, and 
dividing up land are included in this class of surveys. The 
surveyor must, for the most part, depend on his general knowl- 
edge of Geometry and Trigonometry, and his own ingenuity, 
for the solutions of problems that arise in location surveys. 

Illustrative Problems. Problem 1. To divide a trian- 
gular field into two parts having a given A 
ratio, by a line through a given vertex. 

Let ABC (Fig. 44) be the triangle, and A the 

given vertex. 

f>j) 
Divide BC at D, so .that equals the given 

ratio , an d draw A B. A BB and ^4 D C are the parts 

O 
required ; for 

ABB-.ABC = BB:BC. 

Problem 2. To cut off from a triangular field a given 
area, by a line parallel to the base. 




SURVEYING 




Let ABC (Fig. 45) be the triangle, and 
let DE be the division line required. 

Then ABC : ABE = AB 2 : AD 2 . 



'ABC : VADE = AB : AD. 

<4 



AD = AB- 



APE 
>ABC' 



iQ Problem 3. To cut off from a 
Fig. 45 triangular field a given fraction of 

the field, by a line from a given point in a side. 

Let ABC (Fig. 46) be the triangle, and P the point from which the 
line PD is to be located so as to cut off, say, one-third the area of the 
triangle. 

AD = AB x AC -T- SAP. 

For ABC:APD = AB X AC : AP x AD = 8:1. 





Fig. 46 

Problem 4. To divide any field into two parts having a 
given ratio, by a line through a given point in the perimeter. 

Let ABCDE (Fig. 47) represent the field, P the given point, and PQ 
the required division line. 

The areas of the whole field and of the required parts having been 
determined, run the line PD from P to a corner D, dividing the field, 
approximately, as required. „ Determine the area PBCD. 

The triangle PDQ represents* the part which must be added to PBCD 
to make the required division. 



LAND SURVEYING 



69 



Hence, 



Area PBQ 
BQ 



i x PB x BQ x sin PBQ. 

2 x areaPPQ 
PD x sin PBQ 



Note. BQ = 



2 x area PDQ 



This perpendicular from 



perpendicular from P on BE 
P on Di? may be run and measured directly. 

Problem 5. To divide a field into a given number of parts, 
so that access to a pond of water is 
given to each. 

Let ABCBE (Fig. 48) represent the field, 
and P the pond. Let it be required to divide 
the field into four parts. Find the area of 
the field and of each part. 

Let AP be one division line. Run PE, 
and find the area APE. Take the differ- 
ence between APE and the area of one 
of the required parts ; this gives the area of 
the triangle PQE, from which QE may be 
found, as in Problem 4. Draw PQ ; PAQ is 
one of the required parts. In like manner, 
PQR and PAS are determined; whence, 
PSR must be the fourth part required. 




EXERCISE VHI 

1. Prom the square A BCD, containing 6 acres 1 rood 24 
perches, part off 3 acres by a line EF parallel to AB. 

2. Prom the rectangle ABCD, containing 8 acres 1 rood 
24 perches, part off 2 acres 1 rood 32 perches by a line EF 
parallel to AD which is equal to 7 chains. Then, from the 
remainder of the rectangle, part off 2 acres 3 roods 25 perches, 
by a line GH parallel to EB. 

3. Part off 6 acres 3 roods 12 perches from a rectangle ABCD, 
containing 15 acres, by a line EF parallel to AB ; AD being 
10 chains. 



70 SURVEYING 

4. From a square ABCD, whose side is 9 chains, part off a 
triangle which shall contain 2 acres 1 rood 36 perches, by a 
line BE drawn from B to the side AD. 

5. From ABCD, representing the rectangle, whose length is 
12.65 chains, and breadth 7.58 chains, part off a trapezoid 
which shall contain 7 acres 3 roods 24 perches, by a line BE 
drawn from B to the side DC. 

6. In the triangle ABC, AB = 12 chains, AC = 10 chains, 
and BC = 8 chains ; part off a trapezoid of 1 acre 2 roods 16 
perches, by the line DE parallel to AB. 

7. In the triangle ABC, AB = 26 chains, AC = 20 chains, 
and BC = 16 chains ; part off a trapezoid of 6 acres 1 rood 24 
perches, by the line DE parallel to AB. 

8. It is required to divide the triangular field ABC among 
three persons whose claims are as the -numbers 2, 3, and 5, so 
that they may all have the use of a watering place at C ; AB 
= 10 chains, AC = 6.85 chains, and CB = 6.10 chains. 

9. Divide the five-sided field A B CHE' among three persons, 
X, Y, and Z, in proportion to their claims, X paying $500, Y 
paying $750, and Z paying $1000, so that each may have the 
use of an interior pond at P, the quality of the land being 
equal throughout. Given AB = 8.64 chains, BC = 8.27 chains, 
CH= 8.06 chains, HE = 6.82 chains, and EA = 9.90 chains. 
The perpendicular PD upon AB = 5.60 chains, PD' upon BC 
= 6.08 chains, PD" upon CH = 4.80 chains, PD'" upon HE 
= 5.44 chains, and PD"" upon EA = 5.40 chains. Assume 
PH as the divisional fence between the shares of X and Z, it 
is required to determine the position of the fences PM and PN 
between the shares of X and Y and between the shares of Y 
and Z. 

10. Divide the triangular field ABC, whose sides AB, AC, 
and BC are 15, 12, and 10 chains, respectively, into three equal 



LAND SURVEYING 71 

parts, by fences EG and DF parallel to BC, without finding 
the area of the field. 

11. Divide the triangular field ABC, whose sides AB, BC, 
and AC are 22, 17, and 15 chains, respectively, among three 
persons, A, B, and C, by fences parallel to the base AB, so that 
A may have 3 acres above the line AB, B 4 acres above A's 
share, and C the remainder. 



SECTION XV 
LAYING OUT THE PUBLIC LANDS 

Reference Lines. The public lands north of the Ohio Biver 
and west of the Mississippi are generally laid out in accord- 
ance with what is known as the rectangular system of 
surveying. First, an initial point is selected with great care, 
and then astronomically established. Through this point a 
principal meridian, or true north and south line, is run by 
means of the solar compass, or the transit with observations 
on Polaris ; and also an east and west line, called a base line. 
Crossing the principal meridian at intervals of 24 miles, both 
north and south of the initial point, are run other east 
and west lines, called standard parallels, or correction lines. 
Northward from the base line and from each of the standard 
parallels, at intervals of 24 miles, both ways from the princi- 
pal meridian, are run true north and south lines, called guide 
meridians. Thus, the land is divided into blocks approxi- 
mately 24 miles square. Six principal meridians have been 
established, in addition to which and connected with which 
there are twenty or more independent meridians in the 
western states and territories. 

Division from Reference Lines; Townships. Within each 
block parallels to the base line, or to a standard parallel, are 
run at intervals of 6 miles. These are called township lines. 



72 



SURVEYING 



At the same intervals are also run north and south lines, 
called range lines. Thus, the tract would be divided into 
townships exactly 6 miles square if it were not for the con- 
vergence of the meridians on account of the curvature of the 
earth. An east and west series of townships is called a tier, 
and a north and south series is called a range. A township 
is designated by giving the number of the tier north or south 
of the base line and the number of the range east or west of 

N 



D \f' 1, 







i l\k I 


'[l 


1 m\ j- 






t" 






\p" 


B 




t' 






\P' 


1 






t 




A 


■ \p 


„ r i ■ i 






V 


r' 


r" | 


G' 1 1 











G ■ 
























D- — ' 


C 


■ 






1 L' 



E 



S 
Fig. 49 

the principal meridian. Thus, T. 3 N., R. 2 W., read town- 
ship three north, range two west, means that the township is 
in the third tier north of the base line, and in the second tier 
west of the principal meridian. 

Let NS (Fig. 49) represent a principal meridian ; WE a base 
line; DL and D'L' standard parallels; GM and G'M' guide 



LAND SURVEYING 



73 



meridians ; rl, r'l', . . . , range lines ; tp, t'p', . . . , township 
lines. If Or is taken as 6 miles, then O'l will be less than 
6 miles. O'k being equal to 6 miles and O'l being less, 
it will be observed that there will be offsets on the base line 
and on standard parallels at intervals of 6 miles. 

Township A would be designated thus : T. 2 1ST., E. 3 E. 
How would townships B and C be designated ? 

Subdivision of Townships. The townships are divided into 
sections approximately 1 mile square, and the sections are 
divided into quarter sections. The 
township, section, and quarter-section 
corners are permanently marked. The 
sections are numbered, beginning at 
the northeast corner, as in Fig. 50, 
which represents a township divided 
into sections. The quarter sections are 
designated, according to their position, 
as N.E., KW., S.E., and S.W. Section FlG . 50 

lines are surveyed in such an order as 

to throw the errors on the northwest quarter sections, which 
are carefully measured and their areas calculated. 

Meander Lines. If in running a line a navigable stream 
or a lake more than 1 mile in length is encountered, it is 
meandered by marking the intersection of the line with the 
bank and running lines from this point along the bank to 
prominent points which are marked, and the lengths and 
bearings of the connecting lines recorded. 

Manual. For detail of methods, see the "Manual of Sur- 
veying Instructions," issued by the Commissioner of the 
General Land Office, at Washington, D.C., for the use of 
Surveyors-General. 



6 

7 
18 
19 
30 
31 


5 
8 
17 
20 
29 
32 


4 
9 

16 
21 
28 
33 


3 
10 
15 

22 
27 
34 


2 
11 
14 
23 
26 
35 


1 

12 
13 

24 
25 
36 



CHAPTER IV 

TRIANGULATION 

SECTION XVI 

DEFINITIONS 

The third method of surveying explained on page 51 is 
an example of triangulation on a small scale. The simple 
principle there involved is elaborately worked out in hydro- 
graphic or topographic surveys, or in the measurement of 
terrestrial arcs, as in the " Transcontinental Triangulation 
and American Arc of the Parallel," recently completed by 
the United States Coast and Geodetic Survey. 

Let F (Fig. 51) represent a point whose position with 
reference to the base line AB is required. Connect AB with 
F by the series of triangles q 

ABC, ACD, ABE, and DEF, 
so that a signal at C is visible 
from A and B, a signal at D * 
visible from A and C, a signal 
at E visible from A and D, 
and a signal at F visible from 
D and E. In the tr ian gle A B C, 
the side AB is known, and the angles at A and B may be 
measured; hence, AC may be computed. In the triangle 
A CD, AC is known, and the angles at A and C may be 
measured ; hence, AD may be computed. In like manner, 
DE and EF or DF may be determined. DF, or some suitable 
line connected with DF, may be measured, and this result 

74 




TRIANGULATION 75 

compared with the computed value to test the accuracy of 
the field measurement. This net or chain of triangles enables 
us to determine the relative position of all the points with 
respect to each other. If the point A is, furthermore, 
astronomically located, and the azimuth of line AB is known, 
then we have sufficient data also to determine the absolute 
geographical position of each of the points. 

Classification. Three orders of triangulation are recognized, 
viz. : primary, in which the sides are from 20 to 190 miles in 
length; secondary, in which the sides are from 5 to 40 miles 
in length, and which connect the primary with the tertiary ; 
tertiary, in which the sides are seldom over 5 miles in length, 
and which bring the survey down to such dimensions as to 
admit of the minor details being filled in by the compass and 
plane table. 

Measurement of Base Lines. Base lines should be measured 
with a degree of accuracy corresponding to their importance. 
Suitable ground must be selected and cleared of all obstruc- 
tions. Each extremity of the line may be marked by cross 
lines on the head of a copper tack driven into a stub which 
-is sunk to the surface of the ground. Poles are set up in 
line about half a mile apart, the alignment being controlled 
by a transit or theodolite placed over one end of the line. 
The preliminary measurement may be made with an iron 
wire about one-eighth of an inch in diameter and 60 meters 
in length, or with a steel chain of the same length. 

The final measurement is made with the tape line, or with 
bars 6 meters long, which are supported upon trestles when in 
use. These bars are placed end to end, and brought to a 
horizontal position, if this can be quickly accomplished; if 
not, the angle of inclination is taken by a sector, or a vertical 
offset is measxired with the aid of a transit, so that the exact 
horizontal distance can be computed. A thermometer is 
attached to each bar, so that the temperature of the bar may 



76 SURVEYING 

be noted and a correction for temperature applied. Some- 
times the bars are laid in melting ice, in which case accuracy 
to at least one five-millionth part of the length measured is 
attainable. 

Measurement of Angles. Angles are measured by means of 
the transit with much greater accuracy than with the com- 
pass, since the reading of the plates of the transit is taken to 
minutes, and by means of microscopes to seconds, while the 
reading of the needle of the compass is to quarter or half- 
quarter degrees. 

In order to eliminate errors of observation and of adjust- 
ment, and errors arising from imperfect graduation of the 
circles, a large number of readings is made and their mean 
taken. Two methods are in use, viz., repetition and series. 

The method of repetition consists essentially in taking as 
many readings of an angle as is desired, the reading in each 
case after the first being from the index of the next preceding 
reading, and then taking the mean. 

The method of series is the one generally used when several 
angles about the same point are to be measured. It con- 
sists essentially in taking the readings successively on each 
station, then reversing the telescope and repeating the obser- 
vations in the reverse order, which completes a series. This 
process is repeated a number"of times, each series beginning 
with a different index. Then the mean of the different series 
is found. 

On account of the curvature of the earth, the sum of the 
three angles of a triangle upon its surface exceeds 180°. 
This spherical excess, as it is called, becomes appreciable only 
when the sides of the triangle are about 5 miles in length. 
To determine the angles of the rectilinear triangle having the 
same vertices, one-third of the spherical excess is generally 
deducted from each spherical angle. 



CHAPTER V 

LEVELING 
SECTION XVII 

DEFINITIONS 

A level surface is a surface parallel with the surface of 
still water, and is, therefore, slightly curved owing to the 
spheroidal shape of the earth. A level line is a line in a 
level surface. The line of apparent level of a place is a 
tangent to the level line at that place. Hence, the line of 
apparent level is perpendicular to the plumb line. 

Leveling is the process of finding the difference of level of 
two places, or the distance of one place above or below a level 
line through another place. 

Corrections for Curvature and Refraction. In ordinary leveling 
no distinction is made between true and apparent levels. In 
precise leveling the difference between the two is measured, 
i.e., correction is made for curvature of the earth. There is 
sometimes also a correction made for refraction of light. 

Let t (Fig. 52) represent the line of apparent level of the 
place P, a the level line, d the diameter 
of the earth ; then c represents the cor- 
rection for curvature. To compute the 
correction for curvature : 

t 2 = c(c + d). {Geometry, § 381.) 

t 2 a 2 

Therefore, c = = — > approxi- 

c + d d ^ 

mately, since c is very small compared 

with • d, and t = a, very nearly. fm. 52 

77 




78 



SURVEYING 



Since d is constant (=7920 miles, nearly), the correction 
for curvature varies as the square of the distance. 

Example. What is the correction for curvature for 1 mile ? 
By substituting in the formula deduced above, 

l 2 . 

miles = 8 inches, nearly. 



_ a _ 
C ~ ~d ~ 7920 



Hence, the correction for curvature for any distance may 
be found in inches, approximately, by multiplying 8 by the 
square of the distance expressed in miles. 

If correction for refraction is also made, it is customary to 
diminish the above by about one-sixth of itself; or, c = f of 8 a 2 . 



SECTION XVIII 
DIFFERENTIAL LEVELING 

Single Setting of Instrument. To find the difference of 
level between two places when both are visible from some 
intermediate point, and the difference of level does not 
exceed 13 feet, only one setting of the level will usually be 
necessary. 

Let A and B (Fig. 53) represent the two places. Set the 
Y level at a station equally distant, or nearly so, from A and 



A' 




Fig. 53 



B, but not necessarily on the line AB. After leveling the 
instrument, bring the telescope to bear upon the rod (p. 38), 
and by signal direct the rodman to move the target until its 
horizontal line is in the line of apparent level of the telescope. 



LEVELING 



79 



Let the rodman now record the height A A' of the target. In 
like manner find BB'. The difference between A A' and BB' 
is the difference of level required. If the instrument is 
equally distant from A and B, or nearly so, the curvature and 
the refraction on the two sides of the instrument balance, and 
no correction for curvature or refraction is necessary. 

Several Settings of Instrument. When both places are not 
visible from the same place, or when the difference of level 
between them is considerable, two or more settings of the 
level may be necessary. 

Let A and D (Fig. 54) represent the two places. Place the 
level midway between A and some intermediate station B. 




Fig. 54 



Find A A' and BB', as in the preceding case, and record the 
former as a backsight and the latter as a foresight. Select 
another intermediate station C, and in like manner find the 
backsight BB" and the foresight CC ; and so continue until 
the place D is reached. 

The difference between the sum, of the foresights and the sum 
of the backsights ivill be the difference of level required. 

Since, BB' + CC + DD' - (AA' + BB" + CC") 
= BB' - BB" + CC - CC" + DD' - AA' 
= B'B" + CC" + D'D - A A' = A' A" - A A' = A A". 



80 SURVEYING 

SECTION XIX 
PROFILE LEVELING 

Definitions. The intersection of a vertical plane with the 
surface of the earth is called a section, or profile. The term 
" profile," however, usually designates the plot, or representa- 
tion of the section on paper. 

Profile leveling is leveling to obtain the data necessary for 
making a profile or plot of any required section. 

A profile is made for the purpose of exhibiting in a single 
view the inequalities of the surface of the ground for great 
distances along the line of some proposed improvement, such 
as a railroad, canal, or ditch, thus facilitating the establishment 
of the proper grades. 

The data necessary for making a ru-ofile of any required 
section are the heights of its different points above some 
assumed horizontal plane, called the datum plane, together 
with their horizontal distances apart or their distances from 
the beginning of the section. 

The position of the datum plane is fixed with reference to 
some permanent object near the beginning of the section, 
called a bench mark, and in order to avoid negative heights 
is assumed at such a distance below this mark that all the 
points of the section shall be above it. 

The heights of the different points of the section above 
the datum plane are determined by means of the level and 
leveling rod ; and the horizontal length of the section is 
measured with an engineer's chain or tape, and divided into 
equal parts, usually 100 feet in length, called stations, marked 
by stakes numbered 0, 1, 2, 3, and so on. 

Where the ground is very irregular, it may be necessary, 
besides taking sights at the regular stakes, to take occasional 
sights at points between them. If, for instance, at a point 



LEVELING 



81 



40 feet in advance of stake 3 (Fig. 55) there is a sudden 
rise or fall in the surface, the height of this point would be 
determined and recorded as at stake 3.40. 

The readings of the rod are ordinarily taken to the nearest 
tenth of a foot, except on bench marks and points called 
turning points, where they are taken to thousandths of a foot. 

A turning point is a point on which the last sight is taken 
just before changing the position of the level, and the first 
sight from the new position of the instrument. A turning 
point may be coincident with one of the stakes, but must 
always be a hard point, so that the foot of the rod may stand 
at the same level for both readings. 




Fig. 55 



Field Work. To explain the method of obtaining the field 
notes necessary for making a profile, let 0, 1, 2, 3, • • •, 11 
(Fig. 55) represent a portion of a section to be leveled and 
plotted. Establish a bench mark at or near the beginning of 
the line, measure the horizontal length of the section, and set 
stakes 100 feet apart, numbering them 0, 1, 2, 3, and so on. 
Place the level at some point, as between 2 and 3, and take 
the reading of the rod on the beneh = 4.832. Let PP' repre- 
sent the datum plane, say 15 feet below the bench mark; then 

15 + 4.832 = 19.832 

is the height of the line of sight AB, called the height of the 
instrument, above the datum plane. 



82 



SURVEYING 



Now take the reading at = 5.2 = A, and subtract the 
same from 19.832, which leaves 14.6 = F, the height of the 
point above the datum plane. Next take sights at 1, 2, 3, 
3.40, and 4, equal, respectively, to 3.7, 3.0, 5.1, 4.8, and 8.3, and 
subtract the same from 19.832 ; the remainders 16.1, 16.8, 




Fig. 56 

14.7, 15.0, and 11.5 are respective heights of the points 1, 2, 
3, 3.40, and 4. * 

Then, as it is necessary to change the "position of the 
instrument, select a point in the neighborhood of 4 suitable 
as a turning point (t.p. in the figure), and take a careful 
reading on it = 8.480 ; subtract this from 19.832, and the 
remainder, 11.352, is the height of the turning point. 

Now carry the instrument forward to a new position, as 
between 5 . and 6, shown in the figure, while the rodman 
remains at t.p.; take a second reading on t.p. = 4.102, and add 
it to 11.352, the height of t.p. above PP'; the sum 15.454 is 
the height of the instrument CD in its new position. 

Take sight upon 5, 6, and 7, equal, respectively, to 4.9, 2.8, 
and 0.904 ; subtract these sights from 15.454, and the results 
10.6, 12.7, and 14.550 are. the heights of the points 5, 6, and 
7, respectively. 

The point 7, being suitable, is made a turning point, and 
the instrument is moved forward to a point between 9 and 10. 
The sight at 7 = 6.870, added to the height of 7 gives 21.420 
as the height of the instrument EF in its new position. The 



LEVELING 



83 



readings at 8, 9, 10, and 11, which are, respectively, 5.4, 3.6, 
5.8, and 9.0, subtracted from 21.420 give the heights of these 
points, namely, 16.0, 17.8, 15.6, and 12.4. 

Proceed in like manner until the entire section is leveled, 
establishing bench marks at intervals along the line to serve 
as reference points for future operations. The bench marks 
should be described with sufficient minuteness to enable any 
one not connected with the survey to locate them easily and 
unmistakably. A record of the work is given in the following 
table : 



Station 


+ s. 


H.I. 


-s. 


H.S. 


Eemabks 


B 


4.832 






15.0 


Bench on rock 20 ft. 







19.832 


5.2 


14.6 


south of 


1 






3.7 


16.1 




2 






3.0 


16.8 




3 






5.1 


14.7 


3 to 3.40 turnpike road 


3.40 






4.8 


15.0 




4 






8.3 


11.5 




t.p. 


4.102 




8.480 


11.352 




- 5 




15.454 


4.9 


10.6 




6 






2.8 


12.7 




7 


6.870 




0.904 


14.550 




8 




21.420 


5.4 


16.0 




9 






3.6 


17.8 




10 






5.8 


15.6 




11 






9.0 


12.4 




B 










Bench on oak stump 


12 










27 ft. N.E. of 12, 


etc. 










etc. 



The first column contains the numbers or names of all the 
points on which sights are taken. The second column con- 
tains the sight taken on the first bench mark, and the sight 
on each turning point taken immediately after the instrument 



84 SURVEYING 

has been moved to a new position. These are called plus 
sights (+ S.) because they are added to the heights of the 
points on which they are taken to obtain the height of the 
instrument given in the third column (H.I.). The fourth 
column contains all the readings except those recorded in the 
second column. These are called minus sights (— S.) because 
they are subtracted from the numbers in the third column to 
obtain all the numbers in the fifth column except the first, 
which is the assumed depth of the datum plane below the 
bench. The fifth column (H.S., height of surface) contains 
the required heights of all the points of the section named 
in the first column together with the heights of all benches 
and turning points. 

Making the Profile. Draw a line PP' (Fig. 56), to repre- 
sent the datum plane, and beginning at some point as P, lay 
off the distances 100, 200, 300, 340, 400* feet, and so on, to the 
right, using some convenient scale, say 200 feet to the inch. 
At these points of division erect perpendiculars equal in length 
to the height of the points 0, 1, 2, 3.40, 4, • • •, given in the 
fifth column of the above field notes, using in this case a larger 
scale, say 20 feet to the inch. Through the extremities of 
these perpendiculars draw the irregular line 0, 1, 2, 3, • • •, 11> 
and the result, with some explanatory figures, is the required 
plot or profile. 

The making of a profile is much simplified by the use of 
profile paper, which may be had by the yard or roll. 

If a horizontal plot is required, the bearings of the differ- 
ent portions of the section must be taken. Such a plot should 
be made, if it will assist in properly understanding the field 
work, or if it is desirable for future reference in connection 
with the field notes. Sometimes both the profile and the plot 
are drawn side by side on the same sheet ; in this case, if 
the line leveled over is hot straight, the profile will be longer 
than the plot. 



LEVELING 



85 



SECTION XX 



TOPOGRAPHIC LEVELING 



The principal object of topographic surveying is to show 
the contour of the ground. This operation, called topographic 
leveling, is performed by representing on paper the curved 
lines in which parallel horizontal planes at uniform distances 
from each other would meet the surface. It is evident that 
all points in the intersection of a horizontal plane with the 
surface of the ground are at the same level. Hence, it is 
necessary only to find points at the same level and join these 
to determine a line of intersection. 

The method commonly employed will be understood by 
reference to Fig. 57. The ground ABCD is divided into 
equal squares, and a numbered 
stake driven at each intersection. 
By means of a level and leveling 
rod the heights of the other sta- 
tions above m and D, the lowest 
stations, are determined. A plot 
of the ground with the intersect- 
ing lines is then drawn, and the -P 
height of each station written as 
in the figure. 

Suppose that the horizontal 
planes are 2 feet apart ; if the 
first passes through m and D, the 

second will pass through p, which is 2 feet above m ; and 
since n is 3 feet above m, the second plane will cut the line 
mn in a point s determined by the proportion mn :ms = 3 : 2. 
In like manner, the points t, q, and r are determined. 

The irregular line tsp ■■• qr represents the intersection of 
the second horizontal plane with the surface of the ground. 




A 



86 SURVEYING 

In like manner, the intersections of the planes, respectively, 
4, 6, and 8 feet above m are traced. The more rapid the 
change in level the nearer these lines approach each other. 

SECTION XXI 
DRAINAGE SURVEYING 

Preliminaries. The locality to be drained should first be 
carefully reconnoitered, with the view of ascertaining the 
general feature of the land so as to enable the surveyor 
properly to locate the drains ; the beginning, route, and 
terminus of which should all be definitely planned. By the 
beginning of a drain is meant its highest point. 

Field Work. The field work is essentially the same for 
under drains and for open drains. The first thing is to 
establish the line of a drain. This includes' the setting of 
stakes at intervals of from 50 feet to 100 feet, and also 
wherever there is an angle in the line ; the bearings and 
lengths of the successive straight-line sections, beginning 
with the instrument set over the beginning of the drain ; 
and the designation by distances of the points of meeting 
of roads and land lines. Levels of the lines are then taken 
in accordance with the method described on pp. 81-83. If 
circumstances will permit, it is sometimes of advantage to 
have the leveling process go hand in hand with the estab- 
lishing of the line. 

Plot and Profile. If a considerable region is to be drained, 
a plot should be made of the entire tract, and on this plot 
should be drawn, in proper position, the lines of the drain 
and its branches. In a suitable place on the sheet should be 
noted the courses of the various sections of the drain and 
the number of linear feet* belonging to each owner of land 
within the tract drained. A profile should also be made, 



LEVELING 



87 



as shown on page 84. From this profile inspection will 
determine whether a single grade will suffice, or whether a 
succession of different grades will be better. 



EXERCISE IX 

1. Find the difference of level of two places from the fol- 
lowing field notes: backsights, 5.2, 6.8, and 4.0; foresights, 
8.1, 9.5, and 7.9. 

2. Stake of the following notes stands at the lowest point 
of a pond to be drained into a creek ; stake 10 stands at the 
edge of the bank, and 10.25 at the bottom of the creek. Make 
a profile, draw the grade line through and 10.25, and fill out 
the columns H.G. and C, the former to show the height of 
grade line above the datum, and the latter, the depth of cut 
at the several stakes necessary to construct the drain. 



Station 


+ s. 


H.I. 


-s. 


H.S. 


H.G. 


C. 


Remarks 


B 


6.000 






25 






Bench on rock 









10.2 




20.8 


0.0 


30 ft. west of 


1 






5.3 






5.3 


stake 1 


2 






4.6 










3 






4.0 










4 






6.8 










5 


4.572 




7.090 










6 






3.9 










7 






2.0 










8 






4.9 










9 






4.3 










10 






4.5 










10.25 






11.8 











Horizontal scale, 2 ch. = 1 in. 
Vertical scale, 20 ft. = 1 in. 



88 



SURVEYING 



3. Find the difference in altitude between the highest 
point and the lowest point of the campus or of a field. 

4. Obtain the data necessary for a profile of a half mile of 
highway, and mate the profile. 

5. Write the proper numbers in the third and fifth columns 
of the following table of field notes, and make a profile of the 
section. 



Station 


+ S. 


H.I. 


-S-. 


H.S. 


Remarks 


B 


6.944 






20 


Bench on post 22 ft. 









7.4 




north of 


1 






5.6 






2 






3.9 






3 






4.6 






t.p. 


3.855 




5.513 




K 


4 






4.9 




- 


5 






3.5 






6 






1.2 







CHAPTER VI 
RAILROAD SURVEYING 

SECTION XXII 
LAYING OUT THE ROUTE 

Preliminary Survey. After it has been decided which of 
several feasible lines is the best, a preliminary survey for 
final location should be made. This should include, among 
other things, data referring to elevations, depressions, streams 
to be crossed, highways, buildings obstructing, character of 
soil, and natural resources affording materials for construc- 
tion ; also data referring to proximity to towns, titles of 
land, rights of way, and so on. 

Establishing the Roadbed. When the general route of a 
railroad has been determined, a middle surface line is run 
With the transit. A profile of this line is determined, as 
on page 84. The leveling stations are commonly 1 chain 
(100 feet) apart. Places of different level are connected by 
a gradient line, which intersects the perpendiculars to the 
datum line at the leveling stations in points determined by 
simple proportion. Hence, the distance of each leveling 
station above or below the level or gradient line which 
represents the position of the roadbed is known. 

SECTION XXIII 

CROSS-SECTION WORK 

Excavations. If the roadbed lies below the surface, an 
excavation is made. Let ACBD (Pig. 58) represent a cross 

89 



90 



SURVEYING 



section of an excavation, f a point in the middle surface line, 
/' the corresponding point in the roadbed, and CD the width 
of the excavation at the bottom. The slopes at the sides are 
commonly made so that A A ' = f A'C, and BB' = f DB'. When 
ff and CD are known, the points A, B, C, and D' are readily 
determined by a level and tape measure. 




If from the area of the trapezoid ABB' A' the areas of 
the triangles AA'C and BB'D are deducted, the remainder 
is the area of the cross section. In like manner the cross 
section at the next station may be • determined. These two 
cross sections, if similar, are the bases of a frustum of a 
quadrangular pyramid whose volume will be the amount of 
the excavation. In case the cross sections are not similar, 
the computations should be made by means of the Prismoidal 
Formula (Geometry, § 733). 

Embankments. If the roadbed lies above the surface, an 
embankment is made, the cross section of which is like that 
of the excavation, but inverted. 




Fig. 59 represents the.cross section of an embankment which 
is lettered so as to show its relation to the excavation of Fig. 58- 



RAILROAD SURVEYING 



91 



SECTION XXIV 



CURVES 



Piinciples. When it is necessary to change the direction 
of a railroad it is done gradually by a curve, usually the 
arc of a circle. Let AF and 
AG (Fig. 60) represent two 
lines to be thus connected. 
Take any convenient length 
AB = AE = t. The inter- 
section of the perpendicu- 
lars BC and EC determines 
the centre C, and the radius 
of curvature BC — r. The 
length of the radius de- 
pends on the angle A and the tangent AB. 
triangle ABC, 

BC 




For, in the right 



Hence, 



tan BA C = — — > or tan i- A 
AB 2 

r — t tan-^1. 



The degree of a railroad curve is the angle subtended at the 
centre of the curve by a chord of 100 feet. If D is the degree 
of a curve and r its radius, 

50 

sin \ D = — } and r = 50 esc \ D. 



For example, a 6° curve has a radius of 955.37 feet. 

Sometimes the topography of the route is such as to neces- 
sitate a successive series of curves of different radii, in which 
case the whole series of curves is called a compound curve, the 
principles involved being the same for each component as for 
a simple curve. 



92 



SURVEYING 



Methods of laying out the Curve. 1. Let Bm (Fig. 61) 
represent a portion of the tangent. It 
is required to find mP, the perpendicu- 
lar to the tangent meeting the curve 
at P. 




Fig. 61 




But 


mP = Bn = CB — Cn. 
CB = r, 


and 


Cn = ^~CP 2 - Pn 2 




= Vr' 2 — t\ 


Hence, 


mP — v — Vr 2 — t' 2 . 



2. It is required to find mP (Fig. 62) 
in the direction of the centre. 



mP = mC 
But mC 



PC. 



Fig. 62 



VlBC' 2 + Bm 2 = V>- 2 + t\ 
Hence, 

mP = Vr 2 + t 2 — r. 



3. Place transits at B and E (Fig. 63). Direct the tele- 
scope of the former to E, 

and of the latter to A . Turn 
each toward the curve the 
same number of degrees, 
and mark P, the point of 
intersection of the lines of 
sight. P is a point in the 
circle to which AB and AE 
are tangents at B and E, 
respectively. 

4. If the degree B of the curve is given and the tangent 
BA at B (Fig. 64), place -the transit at B and direct the tele- 
scope toward A. Turn off successively the angles ABP, PBP', 




Fig. 63 



RAILROAD SURVEYING 



93 



P'BP", • • -, each equal to 
\D, and take BP, PP', P'P", 
■ ■ ■, each 100 feet, the length 
of the tape. Then, P, P', 
P", ■ ■ ■ lie on the required 
curve. 

If the angle A and the 
tangent distance BA = t 
are given, D can be found 
from the formulas 

50 




Fig. 64 



sin £ D = — > and r = t tan \ A. 

50 
Whence, sin \ D = — cot \ A. 



EXERCISE X 

1. The cross-section areas at five stations, 100 feet apart, 
of a railroad cut are, respectively, 576.8 square feet, 695.1 
square feet, 809.5 square feet, 652.0 square feet, and 511.7 
square feet. Compute the volume of material in this portion 
of the cut : (i) on the hypothesis that the cross sections are 
similar; (ii) on the hypothesis that they are dissimilar, the 
alternate cross sections being regarded as mid-sections. 

2. Find the radius of a curve of 1°, of 2°, of 3°, of 4°, of 5°. 

3. Two adjacent straight sections of a railroad form an 
angle of 148° 16'. They are joined by a curve touching each 
of them at the distance of 388 feet from the vertical point. 
Find the radius and the degree of the curve. 

4. Lay out a curve by the first or second method, and 
check the work by means of one of the transit methods. 



CHAPTER VII 
CITY SURVEYING . 
SECTION XXV 
FIELD WORK 

Instruments. Since the principles in city surveying are 
essentially the same as those in land surveying, instruments 
of the same general character as the instruments already 
described may be used, except that in this class of work the 
ordinary compass and the chain are seaside. For the smaller 
cities, an instrument such as the surveyor's transit is suffi- 
cient in accuracy for the purposes of angle measurement and 
for leveling. However, when extreme accuracy is demanded, 
as in the case of large cities, specially made instruments 
should be used : a transit reading to 30 seconds, or even to 
10 seconds ; a high-grade Y level of at least 20-inch length ^ 
and a standard tape, tested for sag and temperature. 

Streets. In most cases the city engineer must take the 
streets as he finds them. When a city has outgrown its 
original plan, if indeed it had any, sheer necessity may 
demand the location of additional streets or changes in 
existing streets. If a proposed town or city is to be laid 
out, the general contour of the ground and location of the 
site determine to a great extent the system of streets to be 
adopted. Experience has shown that wherever possible a 
rectangular system of street lines, with a few well-located 
diagonal streets, is the most satisfactory. Streets ordinarily 
vary in width from 50 to 100 feet, and each sidewalk from 7 

94 



CITY SURVEYING 



95 



Vincent 












































Simpson 






.570 ' 






Athletic 


9) 


s 


Field 


< 







~1 




C-O-l-1- 6-ff-e Sewer 



i^r^^^ s i t^t^ TQ"^^ ^: 



Fi<;. 65 



to 15 feet. The principal improvements of streets are grad- 
ing, paving, setting curbs, laying sidewalks, constructing 
sewers, and laying water pipes. 



96 SURVEYING 

The field work necessary for all these may be included 
under the heads of leveling, locating lines, and locating 
points, which have already been described. 

Blocks and Lots. There is no established rule for the 
size of either blocks or lots. Fig. 65 gives some idea of their 
dimensions. The location of a block is described by refer- 
ence to the streets which bound it. A lot is described by 
number and block, or by number alone, or by giving the 
location and length of its bounding lines. The co-ordinate 
system of location of points, described on page 53, has 
much in its favor for use in city surveying. Monuments 
at points of reference and at intersections of streets and 
corners of lots should be of permanent character, and set 
with extreme care. 

SECTION XXVI 
OFFICE WORK 

Plots. Among the more important plots that should be 
prepared by the city engineer are a complete city map, drawn 
to scale, showing the streets and alleys, blocks and lots, with 
dimensions, and the location of railroads, street-car lines, sew- 
age system, water-pipe lines, and so on ; a topographical map 
of the entire city, including as may be found desirable por- 
tions of the surrounding region ; a profile map of the streets. 
These are made from the field notes, which should be amply 
and carefully prepared.. 

Records. No work of importance, whether done in the field 
or in the office, should fail to be recorded in some perma- 
nent form. Field notes, computations, plots, and copies of 
work specially prepared should be properly indexed and filed 
away. 



ANSWERS 97 

v 

SURVEYING 

Exercise II. Page 22 
2. 540°. 4. N. 51° 30' E. 

Exercise III. Page 27 
2. 360°. 3. 235 ft. 3.8 in. 

Exercise V. Page 55 

1. 8 a. 64 p. 6. 13 a. 6^ i>. 11. 4 a. 35 p. 

2. 16 a. 74|| p. 7. 2 a. 58| p. 12. 4 a. 110 p. 

3. 4 a. 5^ r- »• 11 a. 157 p. 13. 6 a. 23|| p. 

4. 115-.fr p. 9. 7.51925. 

5. 3 a. 78 p. 10. 13.0735. 

Exercise VI. Page 64 



1. 


2 a. 26 p. 


3. 8 a. 54 p. 


5. 2 a. 78 p. 


7. 


5 a. 42 p. 


2. 


20 a. 12 p. 


4. 3 a. 122 p. 


6. 6 a. 2 p. 


8. 


2 a. 151 p. 



Exercise VII. Page 66 
1. 2 a. 12| p. 2. 98 a. 92 p. 

Exercise VIII. Page 69 

1. AE=S.lb ch. 4. AE = 5.50 ch. 

2. AE = 3.50 ch. ; 5. CE = 4.456 ch. 

EG = 3.42 ch. 6 AI) _ 2 .275 ch. ; BE = 1.82 ch. 

3. AE = 4.55 ch. 7. ylZ> = 4.51 ch.; BE = 3.61 ch. 

8. The distances on ^4B are 2 ch., 3 ch., and 5 ch. 

9. EM (on EA) = 2.5087 ch. ; AN (on AB) = 6.4390 ch. 



98 



SURVEYING 



10. Let EG>BF; then AE = 12.247 ch., AG = 0.798 ch., AD = 8.660 

ch., AF = 6.928 ch. 

11. LelDG>EF; then CG = 14.862 ch., CD = 13.113 ch., CF= 11.404 

ch., CE= 10.062 ch. 

Exercise IX. Page 87 

1. 9.5. 

2. Column H.G. 20.8, 20.4, 20.0, 19.6, 19.2, 18.8, 18.4, 18.0, 17.6, 

17.2, 16.8, 16.7. 
Column C. 0.0, 5.3, 6.4, 7.4, 5.0, 5.1, 6.2, 8.5, 6.0, 7.0, 7.2, 0.0. 




8 9 10 10.25 



5. Third column : 26.944 opposite ; 25.286 opposite 4. 

Fifth column : 20, 19.5, 21.3, 23, 22.3, 21.431, 20.4, 21.8, 24.1. 




Exercise X. Page 93 

1. 9986.5 cu. yd.; 9994.9 cu. yd. 

2. 5730 ft.; 2865 ft.; 1910 ft.; 1433 ft.; 1146 ft. 

3. 1365 ft.; 4° 11' 53". 



FIVE -PLACE 



Logarithmic and Trigonometric 



TABLES 



ARRANGED BY 



G. A. WENTWORTH, A.M. 



G. A. HILL, A.M. 



Boston, U.S.A., and London 

PUBLISHED BY GINN & COMPANY 

1903 






Entered according to Act of Congress, in the year 1882, by 

G. A. WENTWORTH and G. A. HILL 
in the office of the Librarian of Congress. a\ Washington 



Copyright, 1895, by G. A. Wentwoeth and G. A. Hill. 




INTRODUCTION. 



1. If the natural numbers are regarded as powers of ten, the 
exponents of the powers are the Common or Briggs Logarithms of 
the numbers. If A and B denote natural numbers, a and b their 
logarithms, then 10 a = A, 10 6 = B ; or, written in logarithmic form, 

log A = a, log B = b. 

2. The logarithm of a product is found by adding the logarithms 
of its factors. 

For, AX B = 10" X 10* = 10" + b . 

Therefore, log (A x B) = a + b = log A + log B. 

3. The logarithm of a quotient is found by subtracting the 
logarithm of the divisor from that of the dividend. 

A 10 a 
For — = — =lo<* — i> 

A 
Therefore, log — = a — 6 = log A — log B. 

Jt> 

4. The logarithm of a power of a number is found by multiply- 
ing the logarithm of the number by the exponent of the power. 

For, A n — (10 a )« = 10 are . 

Therefore, log A n — an = n log A . 

5. The logarithm of the root of a number is found by dividing 
the logarithm of the number by the index of the root. 

For, y/A = \/To« = 10". 

Therefore, log yfI = - = ^^ • 

n n 

6. The logarithms of 1, 10, 100, etc., and of 0.1, 0.01, 0.001, 
etc., are integral numbers. The logarithms of all other numbers 
are fractions. 



IV LOGARITHMS. 



For, 10° = 1, hence log 1 = 

10 1 = 10, hence log 10 = 1 

102 - ioo, hence log 100 = 2 

10 3 = 1000, hence log 1000 = 3 



10-i = 0.1, hence log 0. 1 = — 1 

10-2= 0.01, hence log 0.01 = —2 

10-s - o.OOl, hence log 0.001 = — 3 

and so on. 

If the number is between 1 and 10, the logarithm is between and 1. 

If the number is between 10 and 100, the logarithm is between 1 and 2. 

If the number is between 100 and 1000, the logarithm is between 2 and 3. 

If the number is between land 0. 1 , the logarithm is between and — 1. 

If the number is between 0.1 and 0.01, the logarithm is between —1 and —2. 

If the number is between 0.01 and 0.001, the logarithm is between —2 and —3. 

And so on. 

7. If the number is less than 1, the logarithm is negative (§ 6), 
but is written in such a form that the fractional part is always positive. 

Tor the number may be regarded as the product of two factors, one of 
which lies between 1 and 10, and the- other is a negative power of 10 ; the 
logarithm will then take the form of a difference whose minuend is a positive 
proper fraction, and whose subtrahend is a positive integral number. 

Thus, 0.48 = 4.8X0.1. 

Therefore (§ 2), log 0.48 = log 4.8 + log 0.1 = 0.68124 - 1. (Page 1.) 

Again, 0.0007 = 7x 0.0001. 

Therefore, log 0.0007 = log 7 + log 0.0001 = 0.84510 - 4. 

The logarithm 0.84510 — 4 is often written 4.84510. 

8. Every logarithm, therefore, consists of two parts : a positive 
or negative integral number, which is called the Characteristic, and 
a positive proper fraction, which is called the Mantissa. 

Thus, in the logarithm 3.52179, the integral number 3 is the characteristic, 
and the fraction .52179 the mantissa. In the logarithm 0.78254 — 2, the inte- 
gral number — 2 is the characteristic, and the fraction 0.78254 is the mantissa. 

9. If the logarithm is negative^ it is customary to change the 
form of the difference so that the subtrahend shall be 10 or a multiple 
of 10. This is done by adding to both minuend and subtrahend a 
number which will increase the subtrahend to 10 or a multiple of 10. 

Thus, the logarithm 0.78254 — 2 is changed to 8.78254 — 10 by adding 8 to 
both minuend and subtrahend. The logarithm 0.92737 — 13 is changed to 
7.92737 — 20 by adding 7 to both minuend and subtrahend. 

10. The following rules are derived from § 6 : — 

If the number is greater than 1, make the characteristic of the 
logarithm one unit less than the number of figures on the left of 
the decimal point. 

If the number is less than 1, make the characteristic of the loga- 
rithm negative, and one unit more than the number of zeros between 
the decimal point and the first significant figure of the given number. 



INTRODUCTION". V 

If the characteristic of a given logarithm is positive, make the 
number of figures in the integral part of the corresponding number 
one more than the number of units in the characteristic. 

If the characteristic is negative, make the number of zeros between 
the decimal point and the first significant figure of the correspond- 
ing number one less than the number of units in the characteristic. 

Thus, the characteristic of log 7849.27 = 3 ; 

the characteristic of log 0.037 = — 2 = 8.00000 — 10. 
If the characteristic is 4, the corresponding number has five figures in its inte- 
gral part. If the characteristic is — 3, that is, 7.00000 — 10, the corresponding 
fraction has two zeros between the decimal point and the first significant figure. 

11. The logarithms of numbers that can be derived one from 
another by multiplication or division by an integral power of 10 
have the same mantissa. 

For, multiplying or dividing a number by an integral power of 10 will 
increase or diminish its logarithm by the exponent of that power of 10 ; and 
since this exponent is an integer, the mantissa of the logarithm will be 
unaffected. 

Thus, log 4.6021 =0.66296. (Page 9.) 

log 460.21 = log (4.6021 X 10 2 ) = log 4.6021 + log 10 2 

= 0.66296 + 2 = 2.66296. 
log 460210 = log (4.6021 X 10 5 ) = log 4.6021 + log 10 5 

= 0.66296 + 5 = 5.66296. 
log 0.046021 = log (4.6021 ■¥ 10 2 ) = log 4.6021 - log 10 2 

= 0.66296 - 2 = 8.66296 - 10. 

TABLE I. 

12. In this table (pp. 1-19) the vertical columns headed N con- 
tain the numbers, and the other columns the logarithms. On page 1 
both the characteristic and the mantissa are printed. On pages 
2-19 the mantissa only is printed. 

The fractional part of a logarithm can be expressed only approx- 
imately, aud in a five-place table all figures that follow the fifth are 
rejected. Whenever the sixth figure is 5, or more, the fifth figure 
is increased by 1. The figure 5 is written when the value of the 
figure in the place in which it stands, together with the succeeding 
figures, is more than 4^, but less than 5. 

Thus, if the mantissa of a logarithm written to seven places is 5328732, it is 
written in this table (a five-place table) 53287. If it is 5328751, it is written 
53288. If it is 5328461 or 5328499, it is written in this table 53285. 

Again, if the mantissa is 5324981, it is written 5325.0 ; and if it is 4999967, it 
is written 50000. 



VI LOGARITHMS. 

This distinction between 5 and 5, in case it is desired to curtail 
still further the mantissas of logarithms, removes all doubt whether 
a 5 in the last given place, or in the last but one followed by a 
zero, should be simply rejected, or whether the rejection should 
lead us to increase the preceding figure by one unit. 

Thus, the mantissa 13925 when reduced to four places should be 1392 ; but 
13925 should be 1393. 

To Find the Logarithm of a Given Number. 

13. If the given number consists of one .or two significant 
figures, the logarithm is given on page 1. If zeros follow the 
significant figures, or if the number is a proper decimal fraction, 
the characteristic must be determined by § 10. 

14. If the given number has three significant figures, it will be 
found in the column headed N (pp. 2-19), and the mantissa of its 
logarithm in the next column to the right, and on the same line. 
Thus, 

Page 2. log 145 = 2.16137, log 14500 = 4.16137. 

Page 14. log 716 = 2.85491, log.0?716 = 9.85491 - 10. 

15. If the given number has four significant figures, the first 
three will be found in the column headed 1ST, and the fourth at the 
top of the page in the line containing the figures 1, 2, 3, etc. The 
mantissa will be found in the column headed by the fourth figure, 
and on the same line with the first three figures. Thus, 

Page 15. log 7682 = 3.88547„ log 76.85 = 1.88564. 
Page 18. log 93280 = 4.96979, log 0.9468 = 9.97626 — 10. 

16. If the given number has five or more significant figures, a 
process called interpolation is required. 

Interpolation is based on the assumption that between two con- 
secutive mantissas of the table the change in the mantissa is directly 
proportional to the change in the number. 

Required the logarithm of 34237. 

The required mantissa is (§ 11), the same as the mantissa for 3423.7 ; there- 
fore it will be found by adding to the mantissa of 3423 seven-tenths of the 
difference between the mantissas for 3423 and 3424. 

The mantissa for 3423 is 53441. 

The difference between the mantissas for 3423 and 3424 is 12. 

Hence, the mantissa for 3423.7 is 53441 + (0.7 x 12) = 53449. 

Therefore, the required logarithm of 34237 is 4.53449. 



INTRODUCTION. Vll 

Required the logarithm of 0.0015764. 

The required mantissa is the same as the mantissa for 1576.4 ; therefore 
it will be found by adding to the mantissa for 1576 four-tenths of the difference 
between the mantissas for 1576 and 1577. 

The mantissa for 1576 is 19756. 

The difference between the mantissas for 1576 and 1577 is 27. 

Hence, the mantissa for 1576.4 is 19756 + (0.4 X 27) = 19767. 

Therefore, the required logarithm of 0.0015764 is 7.19767 — 10. 

Eequired the logarithm of 32.6708. 

The required mantissa is the same as the mantissa for 3267.08; therefore 
it will be found by adding to the mantissa for 3267 eight-hundredths of the 
difference between the mantissas for 3267 and 3268. 

The mantissa for 3267 is 51415. 

The difference between the mantissas for 3267 and 3268 is 13. 

Hence, the mantissa for 3267.08 is 51415 + (0.08 X 13) = 51416. 

Therefore, the required logarithm of 32.6708 is 1.51416. 

17. When the fraction of a unit in the part to be added to the 
mantissa for four figures is less than 0.5 it is to be neglected ; when 
it is 0.5 or more than 0.5 it is to be taken as one unit. 

Thus, in the first example, the part to be added to the mantissa for 3423 is 
8.4, and the .4 is rejected. In the second example, the part to be added to the 
mantissa for 1576 is 10.8, and 11 is added. 



To Find the Antilogarithm ; that is, the Number Corre- 
sponding to a Given Logarithm. 

) 
18. If the given mantissa can be found in the table, the first 

three figures of the required number will be found in the same line 
with the mantissa in the column headed 1ST, and the fourth figure at 
the top of the column containing the mantissa. 

The position of the decimal point is determined by the charac- 
teristic (§ 10). 

Find the number corresponding to the logarithm 0.92002. 

Page 16. The number for the mantissa 92002 is 8318. 

The characteristic is ; therefore, the required number is 8.318. 

Find the number corresponding to the logarithm 6.09167. 

Page 2. The number for the mantissa 09167 is 1235. 

The characteristic is 6 ; therefore, the required number is 1235000. 

Find the number corresponding to the logarithm 7.50325 — 10. 

Page 6. The number for the mantissa 50325 is 3186. 

The characteristic is — 3 ; therefore, the required number is 0.003186. 



Vlll LOGARITHMS. 

19. If the given mantissa cannot be found in the table, find 
in the table the two adjacent mantissas between which the given 
mantissa lies, and the four figures corresponding to the smaller of 
these two mantissas will be the first four significant figures of the 
required number. If more than four figures are desired, they may 
be found by interpolation, as in the following examples : 

Find the number corresponding to the logarithm 1.48762. 

Here the two adjacent mantissas of the table, between which the given man- 
tissa 48762 lies, are found to be (page 6) 48756 and 48770. The corresponding 
numbers are 3078 and 3074. The smaller of these, 3073, contains the first four 
significant figures of the required number. 

The difference between the two adjacent mantissas is 14, and the difference 
between the corresponding numbers is 1. 

The difference between the smaller of the two adjacent mantissas, 48756, 
and the given mantissa, 48762, is 6. Therefore, the number to be annexed to 
3073 is T 6 ¥ of 1 = 0.428, and the fifth significant figure of the required number 
is 4. 

Hence, the required number is 30.734. 

Find the number corresponding to the logarithm 7.82326 — 10. 

The two adjacent mantissas between which 82326 lies are (page 13) 82321 
and 82328. The number corresponding to the mantissa 82321 is 6656. 

The difference between the two adjacent mantissas is 7, and the difference 
between the corresponding numbers is 1. 

The difference between the smaller mantissa, 82321, and the given mantissa, 
82326, is 5. Therefore, the number to be annexed to 6656 is f of 1 = 0.7, and 
the fifth significant figure of the required number is 7. 

Hence, the required number is 0.0066567. 

In using a five-place table the numbers corresponding to man- 
tissas may be carried to five significant figures, and in the first 
part of the table to six figures.* 

20. The logarithm of the reciprocal of a number is called the 
Cologarithm of the number. 

If A denotes any number, then 

colog A = log — = log 1 — log A (§ 3) = — log A. 

Hence, the cologarithm of a number is equal to the logarithm of 
the number with the minus sign prefixed, which sign affects the 
entire logarithm, both characteristic and mantissa. 

*In most tables of logarithms proportional parts are given as an aid to 
interpolation ; but, after a little practice, the operation can be performed nearly 
as rapidly without them. Their omission allows a page with larger-faced type 
and more open spacing, and consequently less trying to the eyes. 



INTRODUCTION. IX 

In order to avoid a negative mantissa in the cologarithm, it is 
customary to substitute for — log A its equivalent 

(10— log A)— 10. 

Hence, the cologarithm of a number is found by subtracting the 
logarithm of the number from 10, and then annexing — 10 to the 
remainder. 

The best way to perform the subtraction is to begin on the left 
and subtract each figure of log A from 9 until we reach the last 
significant figure, which must be subtracted from 10. 

If log A is greater in absolute value than 10 and less than 20, 
then in order to avoid a negative mantissa, it is necessary to write 
— log A in the form 

(20 - log A)— 20. 

So that, in this case, colog A is found by subtracting log A from 
20, and then annexing — 20 to the remainder. 

Find the cologarithm of 4007. 

10 -10 

Page 8. log 4007 = 3.60282 

colog 4007= 6.39718 — 10 

Find the cologarithm of 103992000000. 

20 -20 

Page 2. log 103992000000 = 11.01700 

colog 103992000000 = 8.98300 — 20 

If the characteristic of log A is negative, then the subtrahend, 
— 10 or — 20, will vanish in finding the value of colog A. 

Find the cologarithm of 0.004007. 

10 - 10 

log 0.004007 = 7.60282 - 10 
colog 0.004007 = 2.39718 

With practice, the cologarithm of a number can be taken from 
the table as rapidly as the logarithm itself. 

By using cologarithms the inconvenience of subtracting the log- 
arithm of a divisor is avoided. For dividing by a number is 
equivalent to multiplying by its reciprocal. Hence, instead of 
subtracting the logarithm of a divisor its cologarithm may be 
added. 



LOGARITHMS. 



Exercises. 



Find the logarithms of : 



1. 6170. 

2. 0.617. 

3. 2867. 



4. 85.76. 

5. 296.8. 

6. 7004. 



7. 0.8694. 

8. 0.5908. 

9. 73243. 



10. 67.3208. 

11. 18.5283. 

12. 0.0042003. 



Find the cologarithms of 



13. 72433. 

14. 802.376. 

15. 15.7643. 



16. 869.278. 

17. 154000. 

18. 70.0426. 



19. 0.002403. 

20. 0.000777. 

21. 0.051828. 



Find the antilogarithms of : 



22. 2.47246. 

23. 7.89081. 

24. 2.91221. 



25. 1.26784. 

26. 3.79029. 

27. 5.18752. 



28. 9.79029-10. 

29. 7.62328 — 10. 

30. 6.15465-10. 



Computation by Logarithms. 



21. (1) Find the value of x, if x = 72214 X 0.08203. 

Page 14. log 72214 = 4.85862 

Page 16. log 0.08203 = 8.91397 — 10 

By §2. logx =3.77259 

Page 11. x = 5923.63 



(2) Find the value of x, if x = 5250 -=- 23487. 



Page 10. 
Page 4. 
Page 4. 


log 5250 
colog 23487 
logx 
.-. X 


= 3.72016 

= 5.62917 - 10 

= 9.34933 - 10 = log 0.22353 

= 0.22353 

7.56 X 4667 X 567 



'899.1X0.00337X23435 

Page 15. log 7.56 = 0.87852 

Page 9. log 4667 = 3.66904 

Page 11. log 567 = 2.75358 

Page 17. colog 899.1 = 7.04619 — 10 

Page 6. colog 0.00337 = 2.47237 

Page 4. colog 23435 = 5.63013 — 10 

Page 5. log x = 2.44983 = log 281.73 

.-. x = 281.73. 



INTRODUCTION. XI 

(4) Find the cube of 376. 

Page 7. log 376 = 2.57519 

Multiply by 3 (§ 4), 3 

Page 10. log 3763 = 7.72557 = log 53158600 

.-. 37 6 3 = 53158600. 

(5) Find the square of 0.003278. 

Page 6. log 0.003278 = 7.51561 — 10 

2 

Page 2. log 0.003278 2 = 15.03122 — 20 = log 0.000010745 

.-.0.0032782= 0.000010745. 

(6) Find the square root of 8322. 

Page 16. log 8322 = 3.92023 

Divide by 2 (§ 5), 2 )3.92023 

log V8322 = 1.96012 = log 91.226 

.-. V8322 = 91.226. 

If the given number is a proper fraction, its logarithm will have 
as a subtrahend 10 or a multiple of 10. In this case, before divid- 
ing the logarithm by the index of the root, both the subtrahend and 
the number preceding the mantissa should be increased by such a 
number as will make the subtrahend, when divided by the index of 
the root, 10 or a multiple of 10. 

(7) Find the square root of 0.000043641. 

Page 8. log 0.000043641 = 5.63989— K 

10 -10 

Divide by 2 (§ 5), 2 )15.63989 — 20 

Page 13. log V 0. 000043641 = 7.81995 — 10 = log 0.0066062 

.-. V0.000043641 = 0.0066062. 

(8) Find the sixth root of 0.076553. 

Page 15. log 0.076553 = 8.88397-10 

50 -50 

Divide by 6 (§ 5), 6 )58.88397 — 60 

Page 13. log V0. 076553 = 9.81400 - 10 = log 0.65163 

.-. \/0.076553 = 0.65163. 



Exercises. 

Find by logarithms the value of : 

45607 5.6123 2.567 

' 31045* ' 0.01987' ' 0.05786' 



Xll LOGARITHMS. 

0.06547 
' 74.938 X 0.05938° 

r 4.657 X 0.03467 
' 3.908 X 0.07189' 

0.0075389 X 0.0079 
' 0.00907 X 009784' 

312 X 7.18 X 31.82 
* 519 X 8.27 X 5.132* 

0.007 x 57.83 X 28.13 
' 9.317 X 00.28 X 476.5* 

5.55 X 0.0007632 X 0.87654 



9. 



2.79 X 0.0009524 X 1.46785 



/(XOOj 

\o.oo; 



r . 003457 X 43.387 X 99.2 X 0.00025 
'" 005824 X 15.724 X 1.38 X 0.00089 



s/ 23.815 X 29.36 X 0.007 X 0.62487 
X/ 0.00072 X 9.236 X 5.924 X 3.0007 



,^1416 X 0.031416 X 0.0031416 



'■Vi 



7285 X 0.017285 X 0.0017285 



TABLE II. 



22. This table (page 20) contains the value of the number nr 
its most useful combinations, and their logarithms. 

Find the length of an arc of 47° 32' 57' 1, in a unit circle. 

47° 32' 57" = 171177" 
log 171177 "= 5.23344 

log \ = 4.68557 - 10 
° a " • ■ 

log arc 47° 32' 57" = 9.91901 - 10 = log 0.82994 
.-. length of arc = 0.82994. 

Find the angle if the length of its arc in a unit circle = 0.54936. 
log 0.54936 =9.73986-10 

colog — = log a" = 5.31443 

° a 

log angle = 5.05429 = log 113316 

.-. angle = 113316" = 31° 28' 36". 



INTRODUCTION. X1H 

23. The relations between arcs and angles given in Table II. 
are readily deduced from the circular measure of an angle. 

In Circular Measure an angle is defined by the equation 

, arc 

angle = — -. — , 
■ radius 

in which the word arc denotes the length of the arc corresponding 
to the angle, when both arc and radius are expressed in terms of 
the same linear unit. 

Since the arc and radius for a given angle in different circles 
vary in the same ratio, the value of the angle given by this equa- 
tion is independent of the value of the radius. 

The angle which is measured by a radius-arc is called a Radian, 
and is the angular unit in circular measure. 

C -J- C 

Since C = 2 ttB, it follows that — = 2 7r, and ■*=- = it. Therefore, 

Jx K 

If the arc = circumference, the angle = 2 nr. 

If the arc = semicircumference, the angle = it. 

If the arc = quadrant, the angle = ^ it. 

If the arc = radius, the angle = 1. 

Therefore, tt = 180°, \ it — 90°, £ it = 60°, ± it = 45°, £ it — 30", 
£ it = 22^°, and so on. 

Since 180° in common measure equals it units in circular measure, 

1° in common measure = zr^ units in circular measure ; 

180 

-....., 180°. 

1 unit in circular measure = m common measure. 

7T 

By means of these two equations, the value of an angle expressed 

in one measure may be changed to its value in the other measure. 

Thus, the angle whose arc is equal to the radius is an angle of 

180° 
1 unit in circular measure, and is equal to , or 57° 17' 45", 

7T 

very nearly. 

TABLE III. 

24. This table (pp. 21-49) contains the logarithms of the trigo- 
nometric functions of angles. In order to avoid negative character- 
istics, the characteristic of every logarithm is printed 10 too large. 
Therefore, — 10 is to be annexed to each logarithm. 

On pages 28-49 the characteristic remains the same throughout 
each column, and is printed at the top and the bottom of the column. 



XIV LOGARITHMS. 

But on pp. 30, 49, the characteristic changes one unit in value at the 
places marked with bars. Above these bars the proper characteristic- 
is printed at the top, and below them at the bottom, of the column. 

25. On pages 28-49 the log sin, log tan, log cot, and log cos, of 
1° to 89°, are given to every minute. Conversely, this part of the 
table gives the value of the angle to the nearest minute when 
log sin, log tan, log cot, or log cos is known, provided log sin or 
log cos lies between 8.24186 and 9.99993, and log tan or log cot 
lies between 8.24192 and 11.75808. 

If the exact value of the given logarithm of a function is not 
found in the table, the value nearest to it is to be taken, unless 
interpolation is employed as explained in § 26. 

If the angle is less than 45° the number of degrees is printed at 
the top of the page, and the number of minutes in the column to 
the left of the columns containing the logarithm. If the angle 
is greater than 45°, the number of degrees is printed at the bottom 
of the page, and the number of minutes in the column to the right 
of the columns containing the logarithms. 

If the angle is less than 45°, the names of its functions are 
printed at the top of the page ; if greater than 45°, at the bottom 
of the page. Thus, 

Page 38. log sin 21° 37' = 9.56631-10. 

Page 45. log cot 36° 53' =10. 12473 -10 = 0. 12473. 

Page 37. log cos 69° 14' = 9.54969 — 10. 

Page 49. log tan 45° 59' = 10.01491 — 10 = 0.01491. 

Page 48. If log cos = 9.87468 — 10, angle = 41° 28'. 

Page 34. If log cot = 9.39353 — 10, angle = 76° 6'. 

If log sin = 9.47760 — 10, the nearest log sin in the table is 9.47774 — 10 
(page 36), and the angle corresponding to this value is 17° 29'. 

If log tan = 0.76520 = 10.76520 — 10, the nearest log tan in the table is 
10.76490 — 10 (page 32), and the angle corresponding to this value is 80° 15'. 

26. If it is desired to obtain the logarithms of the functions of 
angles that contain seconds, or to obtain the value of the angle in 
degrees, minutes, and seconds, from the logarithms of its functions,, 
interpolation must be employed. Here it must be remembered 
that, 

The difference between two consecutive angles in the table 
is 60". 

Log sin and log tan increase as the angle increases ; log cos and 
log cot diminish as the angle increases. 



INTRODUCTION. XV 

Find log tan 70° 46' 8". 

Page 37. log tan 70° 46' = 0.45731. 

The difference between the mantissas of log tan 70° 46' and log tan 70° 47' 
is 41, and ^ of 41 — 5. 

As the function is increasing, the 5 must be added to the figure in the fifth 
place of the mantissa 45731 ; and 

Therefore log tan 70° 46' 8'' = 0.45736. 

Find log cos 47° 35' 4". 

Page 48. log cos 47° 35' = 9.82899 — 10. 

The difference between this mantissa and the mantissas of the next log cos 
is 14, and ^ of 14 = 1. 

As the function is decreasing, the 1 must be subtracted from the figure in the 
fifth place of the mantissa 82899 ; and 

Therefore log cos 47° 35' 4" = 9.82898 — 10. 

Find the angle for which log sin = 9.45359 — 10. 

Page 35. The mantissa of the nearest smaller log sin in the table is 45334. 

The angle corresponding to this value is 16° 30'. 

The difference between 45334 and the given mantissa, 45359, is 25. 

The difference between 45334 and the next following mantissa, 45377, is 43, 
and ff of 60" = 35". 

As the function is increasing, the 35" must be added to 16° 30'; and the 
required angle is 16° 30' 35". 

Find the angle for which log cot = 0.73478. 

Page 32. The mantissa of the nearest smaller log cot in the table is 73415. 

The angle corresponding to this value is 10° 27'. 

The difference between 73415 and the given mantissa is 63. 

The difference between 73415 and the next following mantissa is 71, and ff- 
of 60" = 53". 

As the function is decreasing, the 53" must be subtracted from 10° 27'; and 
the required angle is 10° 26' 7". 



Find 



Exercises. 

1. log sin 30° 8' 9". 9. log tan 25° 27' 47". 

2. log sin 54° 54' 40". 10. log cos 56° 11' 57". 

3. log cos 43° 32' 31". 11. log cot 62° 0' 4". 

4. log cos 69° 25' 11". 12. log cos 75° 26' 58". 

5. log tan 32° 9' 17". 13. log tan 33° 27' 13". 

6. log tan 50° 2' 2". 14. log cot 81° 55' 24". 

7. log cot 44° 33' 17". 15. log tan 89° 46' 35". 

8. log cot 55° 9' 32". 16. log tan 1° 25' 56". 



XVI LOGARITHMS. 

Find the angle A if 

17. log sin A- 9.70075. 25. log cos A — 9.40008. 

18. log sin A= 9.91289. 26. log cot A = 9.78815. 

19. logcos^4= 9.86026. 27. log cos A - 9.34301. 

20. log cos A= 9.54595. 28. log tan A = 10.52288. 

21. logtan^= 9.79840. 29. log cot A = 9 65349. 

22. log tan J. = 10.07671. 30. log sin A = 8.39316. 

23. log cot A = 10.00675. 31. log sin A = 8.06678. 

24. log cot A= 9.84266. 32. log tan A = 8.11148. 

27. If log sec or log esc of an angle is desired, it may be found 
from the table by the formulas, 

sec A = 7 ; hence, log sec A = colog cos A. 

cos A ° 

esc A = — - ; hence, log esc A = colog sin A. 

sin A 

Page 31. log sec 8° 28' = colog cos 8° 28' = 0.00476. 
Page 42. log esc 59° 36' 44" = colog sin 59° 36' 44" = 0.06418. 

28. If a given angle is between 0° and 1°, or between 89° and 90°; 
or, conversely, if a given log sin or log cos does not lie between the 
limits 8.24186 and 9.99993 in the table; or, if a given log tan or 
log cot does not lie between the limits 8.2 ; |192 and 11.75808 in the 
table ; then pages 21-24 of Table III. must be used. 

On page 21, log sin of angles between 0° and 0° 3', or log cos of 
the complementary angles between 89° 57' and 90°, are given to 
every second; for the angles between 0° and 0° 3', log tan = log sin, 
and log cos = 0.00000 ; for the angles between 89° 57' and 90°, 
log cot = log cos, and log sin = 0.00000. 

On pages 22-24, log sin, log'tan, and log cos of angles between 
0° and 1°, or log cos, log cot, and log sin of the complementary 
angles between 89° and 90°, are given to every 10". 

Whenever log tan or log cot is not given, they may be found by 
the formulas, 

log tan = colog cot. • log cot = colog tan. 

Conversely, if a given log tan or log cot is not contained in the 
table, then the colog must be found ; this will be the log cot or 
log tan, as the case may be, and will be contained in the table. 

On pages 25-27 the logarithms of the functions of angles 
between 1° and 2°, or between 88° and 90°, are given in the manner 
employed on pages 22-24. These pages should be used if the angle 
lies between these limits, and if not only degrees and minutes, but 
degrees, minutes, and multiples of 10" are given or required. 



INTRODUCTION. XV11 

When the angle is between 0° and 2°, or 88° and 90°, and a 
greater degree of accuracy is desired than that given by the table, 
interpolation may be employed ; but for these angles interpolation 
does not always give true results, and it is better to use Table IV. 

Find log tan 0° 2' 47", and log cos 89° 37' 20". 

Page 21. log tan 0° 2' 47" = log sin 0° 2" 47" = 6.90829 - 10. 
Page 23. log cos 89° 37' 20" = 7.81911 — 10. 

Find log cot 0° 2' 15". 

10 -10 

Page 21. log tan 0° 2' 15" = 6.81591-10 
Therefore, log cot 0° 2' 15" = 3.18409 

Find log tan 89° 38' 30". 

10 -10 

Page 23. log cot 89° 38' 30" = 7.79617 — 10 
Therefore, log tan 89° 38' 30" = 2.20383 

Find the angle for which log tan = 6.92090 — 10. 

Page 21. The nearest log tan is 6.92110 — 10. 
The corresponding angle for which is 0° 2' 52". 

Find the angle for which log cos = 7.70240 — 10. 

Page 22. The nearest log cos is 7.70261 — 10. 
Ihe corresponding angle for which is 89° 42' 40". 

Find the angle for which log cot = 2.37368. 

This log cot is not contained in the table. 
The colog cot = 7.62632 — 10 = log tan. 

The log tan in the table nearest to this is (page 22) 7.62510— 10, and the 
angle corresponding to this value of log tan is 0° 14' 30". 

29. If an angle x is between 90° and 360°, it follows, from 
formulas established in Trigonometry, that, 

between 90° and 180°, between 180° and 270°, 

log sin x = \og sin (180° — x), log sin a; = log sin (x — 180°)„, 

log cos x = log cos (180° — x) n , log cos x = log cos (x — 180°)„, 

log tan x = log tan (180° — x) n , log tan x = log tan (x — 180°), 

log cot x = log cot (180° — x) n ; log cot x = log cot (x — 180°) ; 

between 270° and 360°, 
log sin £ = log sin (360° — x) n , 
log cos # = log cos (360° — x), 
log tan x = log tan (360° — x) n , 
log cot cc = log cot (360° — x) n . 



XV111 LOGARITHMS. 

The letter n is placed (according to custom) after the logarithms 
of those functions which are negative in value. 

The above formulas show, without further explanation, how to 
find by means of Table III. the logarithms of the functions of any 
angle between 90° and 360°. 

Thus, log sin 137° 45' 22" = log sin 42° 14' 38" = 9.82756 — 10. 
log cos 137° 45' 22" = log„ cos 42° 14' 38" = 9.86940 n — 10. 
log tan 137° 45' 22" = log„ tan 42° 14' 38" = 9.95815„ — 10. 
log cot 137° 45' 22" = log,, cot 42° 14' 38" = 0.04185„. 
log sin 209° 32' 50" = log, sin 29° 32' 50" = 9.69297 n — 10. 
log cos 330° 27' 10" = log cos 29° 32' 50" = 9.93949 — 10. 

Conversely, to a given logarithm of a trigonometric function 
there correspond between 0° and 360° four angles, one angle in 
each quadrant, and so related that if x denote the acute angle, the 
other three angles are 180° —x, 180° +x, and 360° — x. 

If besides the given logarithm it is known whether the function 
is positive or negative, the ambiguity is confined to two quadrants, 
therefore to two angles. 

Thus, if the log tan = 9.47451 — 10, the angles are 16° 36' 17" in Quadrant I. 
and 196° 36' 17" in Quadrant III. ; but if the log tan = 9.47451„— 10, the angles 
are 163° 23' 43" in Quadrant II. and 343° 23' 43" in Quadrant IV. 

To remove all ambiguity, further conditions . are required, or a 
knowledge of the special circumstances connected with the problem 
in question. 

TABLE IV. 

30. This table (page 50) must be used when great accuracy is 
desired in working with angles between 0° and 2°, or between 88° 
and 90°. 

The values of S and T are such that when the angle a is 
expressed in seconds, 

S = log sin a — log a", 
T = log tan a — log a". 

Hence follow the formulas given on page 50. 

The values of S and T are printed with the characteristic 10 too 
large, and in using them — 10 must always be annexed. 



Find log sin 0° 58' 17". 

0° 58' 17" = 3497" 
log 3497 = 3.54370 

S = 4.68555 — 10 
log sin 0° 58' 17" = 8.22925 - 10 



Find log cos 88° 26' 41.2". 

90° - 88° 26' 41.2" = 1° 33' 18.8" 
= 5598.8" 
log 5598.8 = 3.74809 

S = 4.68552 - 10 
log cos 88° 26' 41.2" = 8.43361 — 10 



INTRODUCTION. 



Find log tan 0° 52' 47.5". 

0° 52' 47.5" = 3167.5" 
log 3167.5 = 3.50072 

T = 4.68561 — 10 , 
log tan 0° 52' 47.5" = 8.18633 - 10 



Find log tan 89° 54' 37.362". 

90° - 89° 54' 37.362" = 0° 5' 22.638" 
= 322.638" 
log 322.638 = 2.50871 

T = 4.68558 — 10 
log cot 89° 54' 37.362" = 7.19429 — *o 
log tan 89° 54' 37.362" = 2.80571 



Find the angle, if log sin = 6. 72306 — 10. 

6.72306-10 
S= 4.68557 — 10 





Subtract, 


2.03749 
109.015" 


= log 109.0K 
= 0° 1' 49.01 


Find the 


angle for which log cot 


= 1.67604. 




colog cot - 
T 
Subtract, 


= 8.32396 - 

= 4.68564 - 

3.63832 

4348.3" 


10 
10 

= log 4348.3 

= 1° 12' 28.3 



Find the angle for which log tan = 1.55407. 

colog tan = 8.44593 — 10 
T = 4.68569 — 10 
Subtract, 3.76024 = log 5757.6 

5757.6" = 1° 35' 57.6", 

and 90° — 1° 35' 57.6" = 88° 24' 2.4". 
Therefore, the angle required is 88° 24' 2.4". 

TABLE V. 

31. This table (p. 51), containing the circumferences and areas 
of circles, does not require explanation. 

TABLE VI. 

32. Table VI. (pp. 52-69). contains the natural sines, cosines, 
tangents, and cotangents of angles from 0° to 90°, at inter- 
vals of 1'. If greater accuracy is desired it may be obtained 
by interpolation. 

Note. In preparing the preceding explanations, we have made free use 
of the Logarithmic Tables by F. G. Gauss. For Table VI. we are indebted 
to D. Carhart. 

TABLE VII. 

33. This table (pp. 70-75) gives the latitude and departure to 
three places of decimals for distances from 1 to 10, corresponding 
to bearings from 0° to 90° at intervals of 15'. 



XX 



LOGARITHMS. 



If the bearing does not exceed 45° it is found in the left-hand 
column, and the designations of the columns under " Distance " 
are taken from the top of the page ; but if the bearing exceeds 
45°, it is found in the right-h.a,n&. column, and the designations 
of the columns under " Distance " are taken from the bottom of 
the page. 

The method of using the table will be made plain by the follow- 
ing examples : — 

(1) Let it be required to find the latitude and departure of the 
course K 35° 15' E. 6 chains. 

On p. 75, left-hand column, look for 35° 15' ; opposite this hearing, in the 
vertical column headed "Distance 6," are found 4.900 and 3.463 under the 
headings ' ' Latitude ' ' and ' ' Departure ' ' respectively. Hence, latitude or 
northing = 4.900 chains, and departure or easting = 3.463 chains. 

(2) Let it be required to find the latitude and departure of the 
course S. 87° W. 2 chains. . 

As the bearing exceeds 45°, we look in the rigttt-hand column of p. 70, and 
opposite 87° in the column marked "Distance 2 " we find (taking the designa- 
tions of the columns from the bottom of the page) latitude = 0.105 chains, and 
departure = 1.997 chains. Hence, latitude or southing = 0.105 chains, and 
departure or westing = 1.997 chains. 

(3) Let it be required to find the latitude and departure of the 
course K 15° 45' W. 27.36 chains. 

In this case we find the required numbers for each figure of the distance 
separately, arranging the work as in the following table. In practice, only the 
last columns under ' ' Latitude ' ' and ' ' Departure ' ' are written. 



Distance. 


Latitude. 


Depaetuee. 


20 = 2 X 10 
7 

0.3 =3 -M0 
0.06 = 6 + 100 


1.925 X 10 = 19.25 

6.737 

2.887 -M0 =0.289 

5.776 -£.100 = 0.058 


0.543 X 10 = 5.43 
1.90 
0.814 -M0 =0.081 
1.628 -7- 100 = 0.016 


27.36 


26.334 


7.427 



Hence, latitude = 26.334 chains, and departure = 7.427 chains. 







TABLE I. 










THE 






COMMON OK BEIGGS LOGAEITHMS 








OF THE 








NATUEAL IUMBEES 








From 1 to 10000. 










1-100 






N log 


N 


log 


N log 


N log 


N log 


1 0. 00 000 


21 


1.32 222 


41 1.61278 


61 1. 7S 533 


81 1.90 849 


2 0. 30 103 


22 


1.34 242 


42 1. 62 325 


62 1. 79 239 


82 1. 91 3S1 


3 0. 47 712 


23 


1.36173 


43 1. 63 347 


63 1. 79 934 


83 1. 91 908 


4 0. 60 206 


24 


1.3S021 


44 1. 64 345 


64 1.80 618 


84 1.92 428 


5 0.69 897 


25 


1. 39 794 


45 1. 65 321 


65 1. 81 291 


85 1. 92 942 


6 0. 77 815 


26 


1.41497 


46 1.66 276 


66 1. 81 954 


86 1.93 450 


7 0. 84 510 


27 


1. 43 136 


47 1.67 210 


67 1. 82 607 


87 1. 93 952 


8 0. 90 309 


28 


1. 44 716 


48 1. 68 124 


68 1. S3 251 


88 1. 94 448 


9 0. 95 424 


29 


1.46 240 


49 1.69 020 


69 1. S3 885 


89 1. 94 939 


10 1.00 000 


30 


1. 47 712 


50 1. 69 897 


70 1. 84 510 


90 1. 95 424 


11 1.04139 


31 


1. 49 136 


51 1.70 757 


71 1. 85 126 


91 1.95 904 


12 1.07 918 


32 


1.50 515 


52 1. 71 600 


72 1. 85 733 


92 1.96 379 


13 1. 11 394 


33 


1. 51851 


53 1.72 428 


73 1.86 332 


93 1.96 848 


14 1.14 613 


34 


1. 53 14S 


54 1. 73 239 


74 1.86 923 


94 1.97 313 


15 1.17 609 


35 


1. 54 407 


55 1.74 036 


75 1. 87 506 


95 1. 97 772 


16 1.20 412 


36 


1. 55 630 


56 1.74 819 


76 1.88 081 


96 1. 98 227 


17 1.23 045 


37 


1. 56 820 


57 1. 75 587 


77 1.8S649 


97 1.98 677 


18 1. 25 527 


38 


1.57 978 


58 1.76 343 


78 1. 89 209 


98 1.99123 


19 1.27 875 


39 


1. 59 106 


59 1. 77 085 


79 1. 89 763 


99 1. 99 564 


20 1. 30 103 


40 


1. 60 206 


60 1. 77 815 


80 1. 90 309 


100 2. 00 000 


N log 


N 


log 


N log 


N log 


N log 



1-100 



2 








100-150 










Sf 


O 


1 


2 


3 4 


5 


6 


7 


8 


9 


100 


00 000 


00 043 


00 087 


00130 00173 


00 217 


00 260 


00 303 


00 346 


00 389 


101 


00 432 


00 475 


00 518 


00 561 00 604 


00 647 


00 689 


00 732 


00 775 


00 817 


102 


00 860 


00 903 


00 945 


00 988 01030 


01072 


0x115 


01157 


01199 


01242 


,103 


01284 


01326 


01368 


01410 014S2 


01494 


01536 


01578 


01620 


01662 


104 


01703 


01745 


01787 


01828 01870 


01912 


01953 


01995 


02 036 


02 078 


105 


02119 


02160 


02 202 


02 243 02 284 


02 325 


02 366 


02 407 


02 449 


02 490 


106 


02 531 


02 572 


02 612 


02 653 02 694 


02 735 


02 776 


02 816 


02 857 


02 898 


107 


02 938 


02 979 


03 019 


03 060 03100 


03 141 


03181 


03 222 


03 262 


03 302 


108 


03 342 


03 383 


03 423 


03 463 03 503 


03 543 


03 583 


03 623 


03 663 


03 703 


109 


03 743 


03 782 


03 822 


03 862 03 902 


03 941 


03 981 


04 021 


04 060 


04100 


HO 


04139 


04179 


04 218 


04 258 04 297 


04 336 


04 376 04 415 


04 454 


04 493 


111 


04 532 


04 571 


04 610 


04 650 04 689 


04 727 


04 766 


04 805 


04 844 


04 883 


112 


04 922 


04 961 


04 999 


05 038 05 077 


05115 


05 154 


05 192 


05 231 


05 269 


113 


05 308 


05 346 


05 3S5 


05 423 05 461 


05 500 


05.538 


05 576 


05 614 


05 652 


114 


05 690 


05 729 


05 767 


05 805 05 843 


05 881 


05 918 


05 956 


05 994 


06 032 


115 


06 070 


06108 


06145 


06183 06 221 


06 258 


06 296 


06 333 


06 371 


06408 


116 


06 446 


06 483 


06 521 


06 558 06 595 


06 633 


06 670 


06 707 


06 744 


06 781 


117 


06 819 


06 856 


06 893 


06 930 06 967 


07 004 


07 041 


07 078 


07115 


07151 


118 


07188 


07 225 


07 262 


07 298 07 335 


07 372 


07 408 


07 445 


07 482 


07 518 


119 


07 555 


07 591 


07 628 


07 664 07 700 


07 737 


07 773 


07 809 


07 846 


07 882 


120 


07 918 


07 954 


07 990 


08 027 08 063 


08 099 


08135 


08171 


08 207 


08 243 


121 


08 279 


08 314 


08 350 


08 386 08 422 


08 458 


08 493 


08 529 


08 565 


08 600 


122 


08 636 


08 672 


08 707 


08 743 08 778 


08 814 


08 849 


08 884 


08 920 


08 955 


123 


08 991 


09 026 


09 061 


09 096 09132 


09167 


09 202 


09 237 


09 272 


09 307 


124 


09 342 


09 377 


09 412 


09 447 09482 


09 517 


09 552 


09 587 


09 621 


09 656 


125 


09 691 


09 726 


09 760 


09 795 09 830 


09 864 


09 890 


09 934 


09 968 


10 003 


126 


10 037 


10 072 


10106 


10140 10175 


10 209 


10 243 


10 278 


10 312 


10 346 


127 


10 380 


10 415 


10 449 


10 483 10 517 


10 551 


10 585 


10 619 


10 653 


10 687 


128 


10 721 


10 755 


10 789 


10 823 10 857 


10 890 


10 924 


10 958 


10 992 


11025 


129 


11059 


11093 


11126 


11160 11193 


11227 


11261 


11294 


11327 


11361 


130 


11394 


11428 


11461 


11494 11528 


11561 


11594 


11628 


11661 


11694 


131 


11727 


11760 


11793 


11826 11860 


11893 


11926 


11959 


11992 


12 024 


132 


12 057 


12 090 


12123 


12156 12189 


12 222 


12 254 


12 287 


12 320 


12 352 


133 


12 385 


12 418 


12 450 


12 483 12 516 


12 548 


12 581 


12 613 


12 646 


12 678 


134 


12 710 


12 743 


12 775 


12 808 12 840 


12 872 


12 905 


12 937 


12 969 


13 001 


135 


13 033 


13 066 


13 098 


13130 13 162 


13194 


13 226 


13 258 


13 290 


13 322 


136 


13 354 


13 386 


13 418 


13 450 13 481 


13 513 


13 545 


13 577 


13 609 


13 640 


137 > 


13 672 


13 704 


13 735 


13 767 13 799 


13 830 


13 862 


13 893 


13 925 


13 956 


138 


13 988 


14 019 


14 051 


14 082 14114 


14145 


14176 


14 208 


14 239 


14 270 


139 


14 301 


14 333 


14 364 


14 395 14 426 


14 457 


14 489 


14 520 


14 551 


14 582 


140 


14 613 


14 644 


14 675 


14 706 14 737 


14 768 


14 799 


14 829 


14 860 


14 891 


141 


14 922 


14 953 


14 983 


15 014 15 045 


15 076 


15106 


15 137 


15 168 


15 198 


142 


15 229 


15 259 


15 290 


15 320 15 351 


15 381 


15 412 


15 442 


15 473 


15 503 


143 


15 534 


15 564 


15 594 


15 625 15 655 


15 685 


15 715 


15 746 


15 776 


15 806 


144 


15 836 


15 866 


15 897 


15 927 15 957 


15 987 


16 017 


16 047 


16 077 


16107 


145 


16137 


16167 


16197 


16 227 16 256 


16 286 


16 316 


16 346 


16 376 


16 406 


146 


16 435 


16 465 


16 495 


16 524 16 554 


16 584 


16 613 


16 643 


16 673 


16 702 


147 


16 732 


16 761 


16 791 


16 820 16 850 


16 879 


16 909 


16 938 


16 967 


16 997 


148 


17 026 


17 056 


17 085 


17114 17143 


17173 


17 202 


17 231 


17 260 


17 2S9 


149 


17 319 


17 348 


17 377 


17 406 17 435 


17 464 


17 493 


17 522 


17 551 


17 580 


150 


17 609 


17 638 


17 667 


17 696 17 725 


17 754 


17 782 


17 811 


17 840 


17 869 


N 


O 


1 


2 


3 4 


5 


6 


7 


8 


9 



100-150 











150-200 








3 


N 





1 


2 


3 


4 


5 


6 


7 


8 


9 


150 


17 609 


17 638 


17 667 


17 696 


17 725 


17 754 


17 782 


17 811 


17 840 


17 869 


151 


17 898 


17 926 


17 955 


17 984 


IS 013 


18 041 


IS 070 


18 099 


18127 


18156 


152 


18184 


18 213 


18 241 


18 270 


18 298 


18 327 


IS 355 


18 384 


18 412 


18 441 


153 


18 469 


18 498 


18 526 


18 554 


18 583 


18 611 


18 639 


IS 667 


18 696 


18 724 


154 


18 752 


18 780 


18 SOS 


18 837 


18 865 


18 893 


18 921 


18 949 


IS 977 


19 005 


155 


19 033 


19 061 


19 0S9 


19117 


19145 


19173 


19 201 


19 229 


19 257 


19 2S5 


156 


19 312 


19 340 


19 368 


19 396 


19 424 


19 451 


19 479 


19 507 


19 535 


19 562 


157 


19 590 


19 618 


19 645 


19 673 


19 700 


19 728 


19756 


19 783 


19 811 


19 838 


158 


19 866 


19 893 


19 921 


19 948 


19 976 


20 003 


20 030 


20 058 


20 0S5 


20112 


159 


20140 


20167 


20194 


20 222 


20 249 


20 276 


20 303 


20 330 


20 358 


20 385 


160 


20 412 


20 439 


20 466 


20 493 


20 520 


20 548 


20 575 


20 602 


20 629 


20 656 


161 


20 683 


20 710 


20 737 


20 763 


20 790 


20 817 


20 844 


20 871 


20 898 


20 925 


162 


20 952 


20 978 


21005 


21032 


21059 


21085 


21112 


21139 


21165 


21192 


163 


21219 


21245 


21272 


21299 


21325 


21352 


21378 


21405 


21431 


21458 


164 


214S4 


21511 


21537 


21564 


21590 


21617 


21643 


21669 


21696 


21722 


165 


21748 


21775 


21801 


21827 


21854 


21880 


21906 


21932 


21958 


21985 


166 


'22 011 


22 037 


22 063 


22 089 


22115 


22 141 


22167 


22194 


22 220 


22 246 


167 


22 272 


22 29S 


22 324 


22 350 


22 376 


22 401 


22 427 


22 453 


22 479 


22 505 


16S 


22 531 


22 557 


22 583 


22 608 


22 634 


22 660 


22 686 


22 712 


22 737 


22 763 


169 


22 789 


22 814 


22 840 


22 866 


22 891 


22 917 


22 943 


22 968 


22 994 


23 019 


170 


23 045 


23 070 


23 096 


23 121 


23147 


23172 


23 19S 


23 223 


23 249 


23 274 


171 


23 300 


23 325 


23 350 


23 376 


23 401 


23 426 


23 452 


23 477 


23 502 


23 528 


172 


23 553 


23 578 


23 603 


23 629 


23 654 


23 679 


23 704 


23 729 


23 754 


23 779 


173 


23 805 


23 830 


23 855 


23 880 


23 905 


23 930 


23 955 


23 980 


24 005 


24 030 


174 


24 055 


24 080 


24105 


24130 


24155 


24180 


24 204 


24 229 


24 254 


24 279 


175 


24 304 


24 329 


24 353 


24 378 


24 403 


24 428 


24 452 


24 477 


24 502 


24 527 


176 


24 551 


24 576 


24 601 


24 625 


24 650 


24 674 


24 699 


24 724 


24 748 


24 773 


177 


24 797 


24 822 


24 846 


24 871 


24 895 


24 920 


24 944 


24 969 


24 993 


25 018 


178 


25 042 


25 066 


25 091 


25 115 


25 139 


25 164 


25 188 


25 212 


25 237 


25 261 


179 


25 285 


25 310 


25 334 


25 358 


25 382 


25 406 


25 431 


25 455 


25 479 


25 503 


180 


25 527 


25 551 


25 575 


25 600 


25 624 


25 648 


25 672 


25 696 


25 720 


25 744 


181 


25 768 


25 792 


25 816 


25 840 


25 864 


25 888 


25 912 


25 935 


25 959 


25 9S3 


182 


26 007 


26 031 


26 055 


26 079 


26102 


26126 


26150 


26174 


26198 


26 221 


183 


26 245 


26 269 


26 293 


26 316 


26 340 


26 364 


26 387 


26 411 


26 435 


26 458 


184 


26 482 


26 505 


26 529 


26 553 


26 576 


26 600 


26 623 


26 647 


26 670 


26 694 


185 


26 717 


26 741 


26 764 


26 788 


26 811 


26 834 


26 858 


26 881 


26 905 


26 928 


186 


26 951 


26 975 


26 99S 


27 021 


27 045 


27 068 


27 091 


27114 


2713S 


27 161 


187 


27184 


27 207 


27 231 


27 254 


27 277 


27 300 


27 323 


27 346 


27 370 


27 393 


188 


27 416 


27439 


27 462 


27 485 


27 508 


27 531 


27 554 


27 577 


27 600 


27 623 


189 


27 646 


27 669 


27 692 


27 715 


27 738 


27 761 


27 784 


27 807 


27 830 


27 852 


190 


27 875 


27 898 


27 921 


27 944 


27 967 


27 989 


28 012 


28 035 


2S058 


28 081 


191 


28103 


28126 


28149 


28171 


2S194 


28 217 


28 240 


28 262 


28 285 


28 307 


192 


28 330 


28 353 


28 375 


28 398 


28 421 


28 443 


28 466 


28 488 


28 511 


28 533 


193 


28 556 


28 578 


28 601 


28 623 


28 646 


28 668 


2S691 


28 713 


28 735 


28 758 


194 


28 780 


28 803 


28 825 


28 847 


28 870 


28 892 


28 914 


28 937 


28 959 


28 981 


195 


29 003 


29 026 


29 048 


29 070 


29 092 


29115 


29137 


29159 


29181 


29 203 


196 


29 226 


29 248 


29 270 


29 292 


29 314 


29 336 


29 358 


29 380 


29 403 


29 425 


197 


29 447 


29 469 


29 491 


29 513 


29 535 


29 557 


29 579 


29 601 


29 623 


29 645 


198 


29 667 


29 68S 


29 710 


29 732 


29 754 


29 776 


29 798 


29 820 


29 842 


29 863 


199 


29 885 


29 907 


29 929 


29 951 


29 973 


29 994 


30 016 


30 038 


30 060 


30 081 


200 


30103 


30125 


30146 


30168 


30190 
4 


30 211 


30 233 


30 255 


30 276 


30 298 


N 


O 


1 


2 


3 


5 


6 


7 


8 


9 



150 - 200 



200 - 250 



N 


O 


1 


2 


3 4 


5 


6 7 8 


9 


200 


30103 


30125 


30146 


30168 30190 


30 211 


30 233 30 255 30 276 


30 298 


201 


30 320 


30 341 


30 363 


30 384 30 406 


30428 


30 449 30 471 30 492 


30 514 


202 


30 535 


30 557 


30 578 


30 600 30 621 


30 643 


30 664 30 685 30 707 


30 728 


203 


30 750 


30 771 


30 792 


30 814 30 835 


30 856 


30 878. 30 899 30 920 


30 942 


204 


30 963 


30 984 


31006 


31027 31048 


31069 


31091 31112 31133 


31154 


205 


31175 


31197 


31218 


31239 31260 


31281 


31302 31323 31345 


31366 


206 


31387 


31408 


31429 


31450 31471 


31492 


31513 31534 31555 


31576 


207 


31597 


31618 


31639 


31660 31681 


31702 


31723 31744 31765 


31785 


208 


31806 


31827 


31 848 


31869 31890 


31911 


31931- 31952 31973 


31994 


209 


32 015 


32 035 


32 056 


32 077 32 098 


32118 


32139 32160 32181 


32 201 


210 


32 222 


32 243 


32 263 


32 284 32 305 


32 325 


32 346 32 366 32 387 


32 408 


211 


32 428 


32 449 


32 469 


32 490 32 510 


32 531 


32 552 32 572 32 593 


32 613 


212 


32 634 


32 654 


32 675 


32 695 32 715 


32 736 


32 756 32 777 32 797 


32 818 


213 


32 838 


32 858 


32 879 


32 899 32 919 


32 940 


32 960 32 980 33 001 


33 021 


214 


. 33 041 


33 062 


33 082 


33102 33 122 


33 143 


33163 33183 33 203 


33 224 


215 


33 244 


33 264 


33 284 


33 304 33 325 


33 345 


33 365 33 385 33 405 


33 425 


216 


33 445 


33 465 


33 486 


33 506 33 526 


33 546 


33 566 33 586 33 606 


33 626 


217 


33 646 


33 666 


33 686 


33 706 33 726 


33 746 


33 766 33 786 33 806 


33 826 


218 


33 846 


33 866 


33 885 


33 905 33 925 


33 945 


33 965 33 985 34 005 


34 025 


219 


34 044 


34 064 


34 084 


34104 34 124 


34143 


34163 34183 34 203 


34 223 


220 


34 242 


34 262 


34 282 


34 301 34 321 


34 341 


34 361 34 380 34 400 


34 420 


221 


34 439 


34 459 


34 479 


34 498 34 518 


34 537 


34 557 34 577 34 596 


34 616 


222 


34 635 


34 655 


34 674 


34 694 34 713 


34 733 


34 753 34 772 34 792 


34 811 


223 


34 830 


34 850 


34 869 


34 889 34 908 


34 928 


34 947 34 967 34 986 


35 005 


224 


35 025 


35 044 


35 064 


35 083 35102 


35 122 

A. 


35141 35160 35180 


35199 


225 


35 218 


35 238 


35 257 


35 276 35 295 


35 315 


35 334 35 353 35 372 


35 392 


226 


35 411 


35 430 


35 449 


35 468 35 488' 


35 507 


35 526 35 545 35 564 


35 583 


227 


35 603 


35 622 


35 641 


35 660 35 679 


35 698 


35 717 35 736 35 755 


35 774 


228 


35 793 


35 813 


35 832 


35 851 35 870 


35 889 


35 908 35 927 35 946 


35 965 


229 


35 984 


36 003 


36 021 


36 040 36059 


36 078 


36 097 36116 36135 


36154 


230 


36173 


36192 


36 211 


36 229 36 248 


36 267 


36 286 36 305 36 324 


36 342 


231 


36 361 


36 380 


36 399 


36 418 36 436 


36 455 


36 474 36 493 36 511 


36530 


232 


36 549 


36 568 


36 586 


36 605 36 624 


36 642 


36 661 36 680 36 698 


36 717 


233 


36 736 


36 754 


36 773 


36 791 36 810 


36 829 


36 847 36 866 36 884 


36 903 


234 


36 922 


36 940 


36 959 


36 977 36 996 


37 014 


37 033 37 051 37 070 


37 088 


235 


37 107 


37125 


37144 


37162 37181 


37199 


37 218 37 236 37 254 


37 273 


236 


37 291 


37 310 


37 328 


37 346 37 365 


37 383 


37 401 37 420 37 438 


37 457 


237 


37 475 


37 493 


37 511 


37 530 37 548 


37 566 


37 585 37 603 37 621 


37 639 


238 


37 658 


37 676 


37 694 


37 712 37 731 


37 749 


37 767 37 785 37 803 


37 822 


239 


37 840 


37 858 


37 876 


37 894 37 912 


37 931 


37 949 37 967 37 985 


38 003 


240 


38 021 


38 039 


38 057 


38 07,5 38 093 


38112 


38130 38148 38166 


38184 


241 


38 202 


38 220 


38 238 


38 256 38 274 


38 292 


38 310 38 328 38 346 


38 364 


242 


38 382 


38 399 


38 417 


38 435 38 453 


38 471 


38 489 38 507 38 525 


38 543 


243 


38 561 


38 578 


38 596 


38 614 38 632 


38 650 


38 668 38 686 38 703 


38 721 


244 


38 739 


38 757 


38 775 


38 792 38 810 


38 828 


38 846 38 863 38 881 


38 899 


245 


38 917 


38 934 


38 952 


38 970 38 987 


39 005 


39 023 39 041 39 058 


39 076 


246 


39 094 


39111 


39129 


39146 39164 


39182 


39199 39 217 39 235 


39 252 


247 


39 270 


39 287 


39 305 


39 322 39 340 


39 358 


39 375 39 393 39 410 


39 428 


248 


39 445 


39 463 


39 480 


39 498 39 515 


39 533 


39 550 39 568 39 585 


39 602 


249 


39 620 


39 637 


39 655 


39 672 39 690 


39 707 


39 724 39 742 39 759 


39 777 


250 


39 794 


39 811 


39 829 


39 846 39 863 


39 881 


39 898 39 915 39 933 


39 950 


N 


O 


1 


2 


3 - 4 


5 


6 7 8 


8 1 



200-250 











250-300 








5 


N 





1 


2 


3 


4 


5 


6 


7 


8 

39 933 


9 


250 


39 794 


39S11 


39 829 


39S46 


39 863 


39 881 


39 898 


39 915 


39 950 


251 


39 967 


39 985 


40 002 


40 019 


40 037 


40 054 


40 071 


40 OSS 


40106 


40123 


252 


40140 


40157 


40175 


40 192 


40 209 


40 226 


40 243 


40 261 


40 278 


40 295 


253 


40 312 


40 329 


40 346 


40 364 


40 381 


40 398 


40 415 


40 432 


40 449 


40466 


254 


40 4S3 


40 500 


40 51S 


40 535 


40 552 


40 569 


40 586 


40 603 


40 620 


40 637 


255 


40 654 


40 671 


40 688 


40 705 


40 722 


40 739 


40 756 


40 773 


40 790 


40807 


256 


40 824 


40S41 


40 85 S 


40S75 


40 892 


40 909 


40 926 


40 943 


40 960 


40976 


257 


40 993 


41010 


41027 


41044 


41061 


4107S 


41095 


41111 


41 128 


41 145 


258 


41 162 


41 179 


41196 


41212 


41229 


41246 


41263 


412S0 


41296 


41313 


259 


41330 


41347 


41363 


41380 


41397 


41414 


41430 


41447 


41464 


414S1 


260 


41497 


41514 


41531 


41547 


41564 


41581 


41597 


41614 


41631 


41647 


261 


41664 


41681 


41697 


41714 


41731 


41747 


41764 


41780 


41797 


41814 


262 


41830 


41847 


41863 


41 S80 


41S96 


41913 


41929 


41946 


41963 


41979 


263 


41996 


42 012 


42 029 


42 045 


42 062 


42 078 


42 095 


42 111 


42 127 


42144 


264 


42 160 


42 177 


42 193 


42 210 


42 226 


42 243 


42 259 


42 275 


42 292 


42 306 


265 


42 325 


42 341 


42 357 


42 374 


42 390 


42 406 


42 423 


42 439 


42 455 


42 472 


266 


42 4SS 


42 504 


42 521 


42 537 


42 553 


42 570 


42 586 


42 602 


42 619 


42 635 


267 


42 651 


42 667 


42 684 


42 700 


42 716 


42 732 


42 749 


42 765 


42 781 


42 797 


26S 


42 813 


42 830 


42 846 


42S62 


42S7S 


42 894 


42 911 


42 927 


42 943 


42 959 


269 


42 975 


42 991 


43 00S 


43 024 


43 040 


43 056 


43 072 


43 OSS 


43 104 


43120 


270 


43 136 


43 152 


43169 


43 1S5 


43 201 


43 217 


43 233 


43 249 


43 265 


43 281 


271 


43 297 


43 313 


43 329 


43 345 


43 361 


43 377 


43 393 


43 409 


43 425 


43 441 


272 


43 457 


43 473 


43 489 


43 505 


43 521 


43 537 


43 553 


43 569 


43 584 


43 600 


273 


43 616 


43 632 


43 64S 


43 664 


43 6S0 


43 696 


43 712 


43 727 


43 743 


43 759 


274 


43 775 


43 791 


43 807 


43S23 


43 83S 


43 854 


43 870 


43 886 


43 902 


43 917 


275 


43 933 


43 949 


43 965 


43 981 


43 996 


44 012 


44 02S 


44 044 


44 059 


44 075 


276 


44 091 


44107 


44 122 


44 13S 


44154 


44170 


44 185 


44 201 


44 217 


44 232 


277 


44 24S 


44 264 


44 279 


44 295 


44 311 


44 326 


44 342 


44 358 


44 373 


44 389 


27S 


44 404 


44 420 


44 436 


44 451 


44 467 


44 4S3 


44 498 


44 514 


44 529 


44 545 


279 


44 560 


44 576 


44 592 


44 607 


44 623 


44 638 


44 654 


44 669 


44 685 


44 700 


280 


44 716 


44 731 


44 747 


44 762 


44 778 


44 793 


44 809 


44 824 


44 840 


44 855 


2S1 


44 871 


44 886 


44 902 


44 917 


44 932 


44 948 


44 963 


44 979 


44 994 


45 010 


282 


45 025 


45 040 


45 056 


45 071 


45 0S6 


45 102 


45 117 


45 133 


45 14S 


45 163 


283 


45 179 


45 194 


45 209 


45 225 


45 240 


45 255 


45 271 


45 286 


45 301 


45 317 


2S4 


45 332 


45 347 


45 362 


45 378 


45 393 


45 408 


45 423 


45 439 


45 454 


45 469 


285 


45 484 


45 500 


45 515 


45 530 


45 545 


45 561 


45 576 


45 591 


45 606 


45 621 


286 


45 637 


45 652 


45 667 


45 682 


45 697 


45 712 


45 728 


45 743 


45 758 


45 773 


287 


45 78S 


45 803 


45 SIS 


45 834 


45 849 


45S64 


45 879 


45 894 


45 909 


45 924 


288 


45 939 


45 954 


45 969 


45 9S4 


46 000 


46 015 


46 030 


46 045 


46 060 


46 075 


289 


46 090 


46105 


46120 


46135 


46150 


46165 


46180 


46195 


46 210 


46 225 


290 


46 240 


46 255 


46 270 


46 285 


46 300 


46 315 


46 330 


46 345 


46 359 


46 374 


291 


46 389 


46 404 


46 419 


46 434 


46 449 


46 464 


46 479 


46 494 


46 509 


46 523 


292 


46 538 


46 553 


46 56S 


46 583 


46 598 


46 613 


46 627 


46 642 


46 657 


46 672 


293 


46 687 


46 702 


46 716 


46 731 


46 746 


46 761 


46 776 


46 790 


46 805 


46 820 


294 


46 835 


46 850 


46 864 


46 879 


46 894 


46 909 


46 923 


46 938 


46 953 


46 967 


295 


46 982 


46 997 


47 012 


47 026 


47 041 


47 056 


47 070 


47 085 


47 100 


47114 


296 


47129 


47 144 


47159 


47173 


47 188 


47 202 


47 217 


47 232 


47 246 


47 261 


297 


47 276 


47 290 


47 305 


47 319 


47 334 


47 349 


47 363 


47 378 


47 392 


47 407 


298 


47 422 


47 436 


47 451 


47 465 


47 480 


47 494 


47 509 


47 524 


47 53S 


47 553 


299 


47 567 


47 582 


47 596 


47 611 


47 625 


47 640 


47 654 


47 669 


47 6S3 


47 69S 


300 


47 712 


47 727 


47 741 


47 756 


47 770 
4 


47 784 


47 799 


47 813 


47 828 


47 842 


N 





1 


2 


3 


5 


6 


7 


8 


9 



250-300 



300-350 



N 


O 


1 


2 


3 4 


5 


6 


7 


8 


9 


300 


47 712 


47 727 


47 741 


47 756 47 770 


47 784 


47 799 


47 813 


47 828 


47 842 


301 


47 857 


47 871 


47 885 


47 900 47 914 


47 929 


47 943 


47 958 


47 972 


47 986 


302 


48 001 


48 015 


48 029 


48 044 48 058 


48 073 


48 087 


48101 


48116 


4S130 


303 


48144 


48159 


4S173 


48187 48 202 


48 216 


48 230 


48 244 


48 259 


48 273 


'304 


48 287 


48 302 


48 316 


48 330 48 344 


48 359 


48 373 


48 387 


48 401 


48 416 


305 


48 430 


48 444 


48 458 


48473 48 487 


48 501 


48 515 


48 530 


48 544 


48 558 


306 


48 572 


48 586 


48 601 


48 615 48 629 


48 643 


48 657 


48 671 


48 686 


48 700 


307 


48 714 


48 728 


48 742 


48 756 48 770 


48 785 


48 799 


48 813 


48 827 


48 841 


308 


48 855 


48 869 


48 883 


48 897 48 911 


48 926 


48 940 


48 954 


48 968 


48 982 


309 


48 996 


49 010 


49 024 


49 038 49 052 


49 066 


49 080 


49 094 


49 108 


49122 


310 


49136 


49150 


49164 


49178 49192 


49 206 


49 220 


49 234 


49 248 


49 262 


311 


49 276 


49 290 


49 304 


49 318 49 332 


49 346 


49 360 


49 374 


49 388 


49 402 


312 


49 415 


49 429 


49 443 


49457 49 471 


49 485 


49 499 


49 513 


49 527 


49 541 


313 


49 554 


49 56S 


49 582 


49 596 49 610 


49 624 


49.638 


49 651 


49 665 


49 679 


314 


49 693 


49 707 


49 721 


49 734 49 748 


49 762 


49 776 


49 790 


49 803 


49 817 


315 


49 831 


49 845 


49 859 


49 872 49 886 


49 900 


49 914 


49 927 


49 941 


49 955 


316 


49 969 


49 982 


49 996 


50 010 50 024 


50 037 


50 051 


50 065 


50 079 


50 092 


317 


50106 


50120 


50133 


50147 50161 


50174 


50188 


50 202 


50 215 


50 229 


318 


50 243 


50 256 


50 270 


50 284 50 297 


50 311 


50 325 


50 338 


50 352 


50 365 


319 


50 379 


50 393 


50 406 


50 420 50433 


50 447 


50 461 


50 474 


50 488 


50 501 


320 


50 515 


50 529 


50 542 


50 556 50 569 


50 583 


50 596 


50 610 


50 623 


50 637 


321 


50 651 


50 664 


50 678 


50 691 50 705 


50 718 


50 732 


50 745 


50 759 


50 772 


322 


50 786 


50 799 


50 813 


50 826 50 840 


50S53 


50 866 


50 880 


50 893 


50 907 


323 


50 920 


50 934 


50 947 


50 961 50 974 


50 987 


51001 


51014 


51028 


51041 


324 


51055 


51068 


51081 


51095 51108 


51121 


51135 


51148 


51162 


51175 


325 


51188 


51202 


51215 


51228 51242 


51255 


5126S 


51282 


51 295 


51 308 


326 


51322 


51335 


51348 


51362 51375 


51388 


51402 


51415 


51 428 


51441 


327 


51455 


51468 


51481 


51495 51508 


51521 


51534 


51548 


51561 


51574 


328 


51587 


51601 


51614 


51627 51640 


51654 


51667 


51680 


51693 


51706 


329 


51720 


51733 


51746 


51759 51772 


51786 


51799 


51812 


51825 


51838 


330 


51851 


51865 


51878 


51891 51904 


51917 


51930 


51943 


51957 


51970 


331 


51983 


51996 


52 009 


52 022 52 035 


52 048 


52 061 


52 075 


52 088 


52101 


332 


52114 


52 127 


52 140 


52153 52166 


52179 


52 192 


52 205 


52 218 


52 231 


333 


52 244 


52 257 


52 270 


52 284 52 297 


52 310 


52 323 


52 336 


52 349 


52 362 


334 


52 375 


52 388 


52 401 


52 414 52 427 


52 440 


52 453 


52 466 


52 479 


52 492 


335 


52 504 


52 517 


52 530 


52 543 52 556 


52 569 


52 582 


52 595 


52 60S 


52 621 


336 


52 634 


52 647 


52 660 


52 673 52 686 


52 699 


52 711 


52 724 


52 737 


52 750 


337 


52 763 


52 776 


52 789 


52 802 52 815 


52 827 


52 840 


52 853 


52 866 


52 879 


338 


52 892 


52 905 


52 917 


52 930 52 943 


52 956 


52 969 


52 982 


52 994 


53 007 


339 


53 020 


53 033 


53 046 


53 058 53 071 


53 084 


53 097 


53110 


53 122 


53135 


340 


53148 


53161 


53173 


53 186 53 199 


53 212 


53 224 


53 237 


53 250 


53 263 


341 


53 275 


53 288 


53 301 


53 314 53 326 


53 339 


53 352 


53 364 


53 377 


53 390 


342 


53 403 


53415 


53 428 


53 441 53 453 


53 466 


53 479 


53 491 


53 504 


53 517 


343 


53 529 


53 542 


53 555 


53 567 53 580 


53 593 


53 605 


53 618 


53 631 


53 643 


344 


53 656 


53 668 


53 681 


53 694 53 706 


53 719 


53 732 


53 744 


53 757 


53 769 


345 


53 782 


53 794 


53 807 


53 820*53 832 


53 845 


53 857 


53 870 


53 882 


53 895 


346 


53 908 


53 920 


53 933 


53 945 53 958 


53 970 


53 983 


53 995 


54 008 


54 020 


347 


54 033 


54 045 


54 058 


54 070 54 083 


54 095 


5410S 


54120 


54 133 


54145 


348 


54158 


54 170 


54183 


54195 54 208 


54 220 


54 233 


54 245 


54 258 


54 270 


349 


54 283 


54 295 


54 307 


54 320 54 332 


54 345 


54 357 


54 370 


54 382 


54 394 


350 


54 407 


54 419 


54 432 


54 444 54 456 


54 469 


54 481 


54 494 


54 506 


54 518 


N 


O 


1 


2 


3 . 4 


5 


6 


7 


8 


9 



300-350 



350-400 



N 





1 


2 


3 


4 


5 


6 


7 


8 


9 


350 


54 407 


54 419 


54 432 


54 444 


54 456 


54 469 


54 481 


54 494 


54 506 


54 518 


351 


54 531 


54 543 


54 555 


54 568 


54 5S0 


54 593 


54 605 


54 617 


54 630 


54 642 


352 


54 654 


54 667 


54 679 


54 691 


54 704 


54 716 


54 728 


54 741 


54 753 


54 765 


353 


54 777 


54 790 


54S02 


54 814 


54 827 


54 839 


54 851 


54 864 


54 876 


54 888 


354 


54 900 


54 913 


54 925 


54 937 


54 949 


54 962 


54 974 


54 986 


54 998 


55 011 


355 


55 023 


55 035 


55 047 


55 060 


55 072 


55 084 


55 096 


55 10S 


55121 


55133 


356 


55145 


55 157 


55 169 


55 182 


55 194 


55 206 


55 218 


55 230 


55 242 


55 255 


357 


55 267 


55 279 


55 291 


55 303 


55 315 


55 32S 


55 340 


55 352 


55 364 


55 376 


358 


55 3SS 


55 400 


55 413 


55 425 


55 437 


55 449 


55 461 


55 473 


55 485 


55 497 


359 


55 509 


55 522 


55 534 


55 546 


55 558 


55 570 


55 582 


55 594 


55 606 


55 618 


360 


55 630 


55 642 


55 654 


55 666 


55 678 


55 691 


55 703 


55 715 


55 727 


55 739 


361 


55 751 


55 763 


55 775 


55 787 


55 799 


55 811 


55 823 


55 835 


55 847 


55 859 


362 


55 871 


55 883 


55 895 


55 907 


55 919 


55 931 


55 943 


55 955 


55 967 


55 979 


363 


55 991 


56 003 


56 015 


56 027 


56 038 


56 050 


56 062 


56 074 


56 086 


56 09S 


364 


56110 


56122 


56134 


56146 


56158 


56170 


56182 


56194 


56 205 


56 217 


365 


56 229 


56 241 


56 253 


56 265 


56 277 


56 289 


56 301 


56 312 


56 324 


56 336 


366 


•56 348 


56 360 


56 372 


56 384 


56 396 


56 407 


56 419 


56 431 


56 443 


56 455 


367 


56 467 


56 47S 


56 490 


56 502 


56 514 


56 526 


56 538 


56 549 


56 561 


56 573 


368 


56 585 


56 597 


56 60S 


56 620 


56 632 


56 644 


56 656 


56 667 


56 679 


56 691 


369 


56 703 


56 714 


56 726 


56 738 


56 750 


56 761 


56 773 


56 7S5 


56 797 


56 SOS 


370 


56 820 


56S32 


56 844 


56 855 


56S67 


56 879 


56 891 


56 902 


56 914 


56 926 


371 


56 937 


56 949 


56 961 


56 972 


56 984 


56 996 


57 008 


57 019 


57 031 


57 043 


372 


57 054 


57 066 


57 078 


57 089 


57101 


57113 


57124 


57136 


57 148 


57159 


373 


57171 


57183 


57194 


57 206 


57 217 


57 229 


57 241 


57 252 


57 264 


57 276 


374 


57 287 


57 299 


57 310 


57 322 


57 334 


57 345 


57 357 


57 36S 


57 380 


57 392 


375 


57403 


57415 


57 426 


57 438 


57449 


57461 


57 473 


57484 


57 496 


57 507 


376 


57 519 


57 530 


57 542 


57 553 


57 565 


57 576 


57 58S 


57 600 


57 611 


57 623 


377 


57 634 


57 646 


57 657 


57 669 


57 680 


57 692 


57 703 


57 715 


57 726 


57 738 


378 


57 749 


57 761 


57 772 


57 784 


57 795 


57 807 


57 818 


57S30 


57 841 


57 852 


379 


57 864 


57S75 


57 8S7 


57S9S 


57 910 


57 921 


57 933 


57 944 


57 955 


57 967 


380- 


57 978 


57 990 


58 001 


58 013 


58 024 


58 035 


58 047 


58 058 


5S070 


58 081 


381 


5S092 


58104 


58115 


58127 


58138 


58149 


58161 


58172 


58184 


58195 


3S2 


58 206 


58 218 


5S229 


58 240 


58 252 


58 263 


58 274 


58 286 


58 297 


58 309 


383 


58 320 


58 331 


58 343 


5S354 


58 365 


58 377 


58 388 


58 399 


58 410 


58 422 " 


384 


58 433 


58 444 


58 456 


58 467 


58 478 


58 490 


58 501 


58 512 


5S524 


58 535 


385 


58 546 


58 557 


58 569 


58 580 


58 591 


58 602 


58 614 


5S625 


58 636 


58 647 


386 


58 659 


58 670 


58 681 


58 692 


58 704 


58 715 


58 726 


58 737 


58 749 


58 760 


387 


58 771 


58 782 


58 794 


5S805 


58 816 


58 827 


5S83S 


58 850 


58 861 


5SS72 


388 


5SSS3 


58 894 


5S906 


58 917 


58 928 


58 939 


58 950 


58 961 


58 973 


58 984 


389 


58 995 


59 006 


59 017 


59 028 


59 040 


59 051 


59 062 


59 073 


59 084 


59 095 


390 


59106 


59118 


59129 


59 140 


59151 


59162 


59173 


59184 


59195 


59 207 


391 


59 218 


59 229 


59 240 


59 251 


59 262 


59 273 


59 284 


59 295 


59 306 


59 318 


392 


59 329 


59 340 


59 351 


59 362 


59 373 


59 3S4 


59 395 


59 406 


59 417 


59 428 


393 


59 439 


59 450 


59 461 


59 472 


59 483 


59 494 


59 506 


59 517 


59 52S 


59 539 


394 


59 550 


59 561 


59 572 


59 583 


59 594 


59 605 


59 616 


59 627 


59 638 


59 649 


395 


59 660 


59 671 


59 682 


59 693 


59 704 


59 715 


59 726 


59 737 


59 748 


59 759 


396 


59 770 


59 7S0 


59 791 


59 802 


59 813 


59 824 


59 835 


59 846 


59 857 


59 868 


397 


59 879 


59 890 


59 901 


59 912 


59 923 


59 934 


59 945 


59 956 


59 966 


59 977 


398 . 


59 988 


59 999 


60 010 


60 021 


60 032 


60 043 


60 054 


60 065 


60 076 


60 086 


399 


60 097 


60108 


60119 


60130 


60141 


60152 


60163 


60173 


60184 


60195 


400 


60 206 


60 217 


60 22S 


60 239 


60 249 


60 260 


60 271 


60 282 


60 293 


60 304 


N 


O 


1 


2 


3 


4 


5 


6 


7 


8 


9 



350-400 



400-450 



N 





1 


2 


3 4 


5 


6 


7 


8 


9 


400 


60 206 


60 217 


60 22S 


60 239 60 249 


60 260 


60 271 


60 2S2 


60 293 


60 304 


401 


60 314 


60 325 


60 336 


60 347 60 35S 


60 369 


60 379 


60 390 


60 401 


60 412 


402 


60 423 


60 433 


60 444 


60 455 60 466 


60 477 


60 4S7 


60 49S 


60 509 


60 520 


403 


60 531 


60 541 


60 552 


60 563 60 574 


60 5S4 


60 595 


60 606 


60 617 


60 627 


-404 


60 63S 


60 649 


60 660 


60 670 60 6S1 


60 692 


60 703 


60 713 


60 724 


60 735 


405 


60 746 


60 756 


60 767 


60 77S 60 7SS 


60 799 


60 S10 


60S21 


60S31 


60 842 


406 


60 S53 


60 863 


60S74 


60SS5 60 895 


60 906 


60 917 


60 927 


60 93S 


60 949 


407 


60 959 


60 970 


60 9S1 


60 991 61002 


61013 


61023 


61034 


61045 


61 055 


40S 


61066 


61077 


610S7 


6109S 61109 


61119 


61130 


61140 


61151 


61162 


409 


61172 


61 183 


61 194 


61204 61215 


61225 


61236 


61247 


61257 


6126S 


410 


6127S 


61289 


61300 


61310 61321 


61331 


61342 


61352 


61363 


61374 


411 


613S4 


61395 


61 405 


61416 61426 


61437 


6144S 


61458 


61469 


61479 


412 


61490 


61500 


61511 


61521 61532 


61542 


61553 


61563 


61574 


615S4 


413 


61595 


61606 


61616 


61627 61637 


6164S 


61658 


61669 


61679 


61690 


414 


61700 


61711 


61721 


61731 61742 


61 752 


61' 763 


61773 


61784 


61794 


415 


61S05 


61 815 


61S26 


61S36 61S47 


61S57 


61S6S 


61S78 


61SSS 


61 899 


416 


61909 


61920 


61930 


61941 61951 


61962 


61972 


619S2 


61993 


62 003 


417 


62 014 


62 024 


62 034 


62 045 62.055 


62 066 


62 076 


62 0S6 


62 097 


62 107 


41S 


62 US 


62 12S 


62 13S 


62 149 62159 


62 170 


62 ISO 


62 190 


62 201 


62 211 


419 


62 221 


62 232 


62 242 


62 252 62 263 


62 273 


62 2S4 


62 294 


62 304 


62 315 


420 


62 325 


62 335 


62 346 


62 356 62 366 


62 377 


62 3S7 


62 397 


62 40S 


62 41S 


421 


62 42S 


62 439 


62 449 


62 459 62 469 


62 4S0 


62 490 


62 500 


62 511 


62 521 


422 


62 531 


62 542 


62 552 


62 562 62 572 


62 5S3 


62 593 


62 603 


62 613 


62 624 


423 


62 634 


62 644 


62 655 


62 665 62 675 


62 6S5 


62 696 


62 706 


62 716 


62 726 


424 


62 737 


62 747 


62 757 


62 767 62 77S 


62 7SS 


62 798 


62 SOS 


62 SIS 


62S29 


425 


62S39 


62S49 


62 859 


62S70 62SS0 


62S90 


62 900 


62 910 


62 921 


62 931 


426 


62 941 


62 951 


62 961 


62 972 62 9S2 


62 992 


63 00"2 


63 012 


63 022 


63 033 


427 


63 043 


63 053 


63 063 


63 073 63 0S3 


63 094 


63 104 


63 114 


63 124 


63134 


42S 


63 144 


63 155 


63 165 


63 175 63 1S5 


63 195 


63 205 


63 215 


63 225 


63 236 


429 


63 246 


63 256 


63 266 


63 276 63 2S6 


63 296 


63 306 


63 317 


63 327 


63 337 


430 


63 347 


63 357 


63 367 


63 377 63 3S7 


63 397 


63 407 


63 417 


63 428 


63 43S 


431 


63 44S 


63 458 


63 468 


63 47S 63 4SS 


63 49S 


63 50S 


63 518 


63 52S 


63 53S 


432 


63 54S 


63 55S 


63 56S 


63 579 63 5S9 


63 599 


63 609 


63 619 


63 629 


63 639 


433 


63 649 


63 659 


63 669 


63 679 63 689 


63 699 


63 709 


63 719 


63 729 


63 739 


434 


63 749 


63 759 


63 769 


63 779 63 7S9 


63 799 


63S09 


63S19 


63 829 


63S39 


435 


63S49 


63S59 


63S69 


63S79 63SS9 


63S99 


63 909 


63 919 


63 929 


63 939 


436 


63 949 


63 959 


63 969 


63 979 63 9SS 


63 99S 


64 00S 


64 01S 


64 02S 


64 03S 


437 


64 04S 


64 058 


64 06S 


64 07S 64 OSS 


64 09S 


6410S 


64 IIS 


6412S 


64137 


438 . 


64 147 


64157 


64 167 


64 177 64 1S7 


64197 


64 207 


64 217 


64 227 


64 237 


439 


64 246 


64 256 


64 266 


64 276 64 2S6 


64 296 


64 306 


64 316 


64 326 


64 335 


440 


64 345 


64 355 


64 365 


64 375 64 3S5 


64 395 


64 404 


64 414 


64 424 


64 434 


441 


64 444 


64 454 


64 464 


64 473- 64 4S3 


64 493 


64 503 


64 513 


64 523 


64 532 


442 


64 542 


64 552 


64 562 


64 572 64 5S2 


64 591 


64 601 


64 611 


64 621 


64 631 


443 


64 640 


64650 


64 660 


64 670 64 6S0 


64 6S9 


64 699 


64 709 


64 719 


64 729 


444 


64 73S 


64 74S 


64 75S 


64 76S 64 777 


64 787 


64 797 


64S07 


64 816 


64S26 


445 


64S36 


64S46 


64 856 


64S65"64S75 


64SS5 


64S95 


64 904 


64 914 


64 924 


446 


, 64 933 


64 943 


64 953 


64 963 64 972 


64 9S2 


64 992 


65 002 


65 011 


65 021 


447 


65 031 


65 040 


65 050 


65 060 65 070 


65 079 


65 0S9 


65 099 


65 10S 


65 IIS 


44S 


65 12S 


65 137 


65 147 


65 157 65 167 


65 176 


65 1S6 


65 196 


65 205 


65 215 


449 


65 225 


65 234 


65 244 


65 254 65 263 


65 273 


65 2S3 


65 292 


65 302 


65 312 


450 


65 321 


65 331 


65 341 


65 350 65 360 


65 369 


65 379 


65 3S9 


65 39S 


65 40S 


X 


O 


1 


2 


3 4 


5 


6 


7 


8 


9 1 



400-450 











450-500 








9 


N 





1 


2 


3 


4 


5 


6 


7 


8 


9 


450 


65 321 


65 331 


65 341 


65 350 


65 360 


65 369 


65 379 


65 389 


65 398 


65 408 


451 


65 418 


65 427 


65 437 


65 447 


65 456 


65 466 


65 475 


65 485 


65 495 


65 504 


452 


65 514 


65 523 


65 533 


65 543 


65 552 


65 562 


65 571 


65 581 


65 591 


65 600 


453 


65 610 


65 619 


65 629 


65 639 


65 648 


65 658 


65 667 


65 677 


65 686 


65 696 


454 


65 706 


65 715 


65 725 


65 734 


65 744 


65 753 


65 763 


65 772 


65 782 


65 792 


455 


65 801 


65 811 


65 820 


65 830 


65 839 


65 849 


65 858 


65 868 


65 877 


65 887 


456 


65S96 


65 906 


65 916 


65 925 


65 935 


65 944 


65 954 


65 963 


65 973 


65 982 


457 


65 992 


66 001 


66 011 


66 020 


66 030 


66 039 


66 049 


66 058 


66 068 


66 077 


458 


66 087 


66 096 


66 106 


66115 


66124 


66134 


66143 


66153 


66162 


66172 


459 


66181 


66191 


66 200 


66 210 


66 219 


66 229 


66 238 


66 247 


66 257 


66 266 


460 


66 276 


66 285 


66 295 


66 304 


66314 


66 323 


66 332 


66 342 


66 351 


66 361 


461 


66 370 


66 380 


66 389 


66 398 


66 408 


66 417 


66 427 


66 436 


66 445 


66 455 


462 


66 464 


66 474 


66 483 


66 492 


66 502 


66 511 


66 521 


66 530 


66 539 


66 549 


463 


66 558 


66 567 


66 577 


66 586 


66 596 


66 605 


66 614 


66 624 


66 633 


66 642 


464 


66 652 


66 661 


66 671 


66 680 


66 689 


66 699 


66 708 


66 717 


66 727 


66 736 


465 


66 745 


66 755 


66 764 


66 773 


66 783 


66 792 


66 801 


66 811 


66 820 


66 829 


466 


66 839 


66 84S 


66 857 


66 867 


66 876 


66 885 


66 894 


66 904 


66 913 


66 922 


467 


66 932 


66 941 


66 950 


66 960 


66 969 


66 978 


66 987 


66 997 


67 006 


67 015 


468 


67 025 


67 034 


67 043 


67 052 


67 062 


67 071 


67 080 


67 089 


67 099 


67 108 


469 


67117 


67127 


67136 


67145 


67154 


67164 


67173 


67182 


67191 


67 201 


470 


67 210 


67 219 


67 228 


67 237 


67 247 


67 256 


67 265 


67 274 


67 284 


67 293 


471 


67 302 


67 311 


67 321 


67 330 


67 339 


67 348 


67 357 


67 367 


67 376 


67 385 


472 


67 394 


67 403 


67 413 


67 422 


67 431 


67 440 


67 449 


67 459 


67 468 


67 477 


473 


67 486 


67 495 


67 504 


67 514 


67 523 


67 532 


67 541 


67 550 


67 560 


67 569 


474 


67 578 


67 587 


67 596 


67 605 


67 614 


67 624 


67 633 


67 642 


67 651 


67 660 


475 


67 669 


67 679 


67 688 


67 697 


67 706 


67 715 


67 724 


67 733 


67 742 


67 752 


476 


67 761 


67 770 


67 779 


67 78S 


67 797 


67 806 


67 815 


67 825 


67 834 


67 843 


477 


67 852 


67 861 


67 870 


67 879 


67 888 


67 897 


67 906 


67 916 


67 925 


67 934 


478 


67 943 


67 952 


67 961 


67 970 


67 979 


67 988 


67 997 


68 006 


68 015 


68 024 


479 


68 034 


68 043 


6S052 


68 061 


68 070 


68 079 


6S0S8 


68 097 


68106 


68115 


480 


68124 


68133 


68142 


68151 


68160 


68169 


68178 


68187 


68196 


68 205 


481 


68 215 


68 224 


68 233 


68 242 


68 251 


68 260 


68 269 


68 27S 


68 287 


68 296 


482 


68 305 


68 314 


68 323 


68 332 


68 341 


68 350 


68 359 


68 368 


68 377 


68 386 


483 


68 395 


68 404 


68 413 


68 422 


68 431 


68 440 


68 449 


68 458 


68 467 


68 476 


484 


68 485 


68 494 


68 502 


68 511 


68 520 


68 529 


68 538 


68 547 


68 556 


68 565 


485 


68 574 


68 583 


68 592 


68 601 


68 610 


68 619 


68 628 


68 637 


68 646 


68 655 


486 


68 664 


68 673 


68 681 


68 690 


68 699 


68 70S 


68 717 


68 726 


68 735 


68 744 


487 


6S753 


6S762 


68 771 


68 780 


68 789 


68 797 


68 806 


68 815 


68 824 


68 833 


488 


6S842 


6S851 


6S860 


6S869 


6S878 


68 886 


68 895 


68 904 


68 913 


68 922 


489 


68 931 


68 940 


68 949 


68 958 


68 966 


68 975 


68 984 


68 993 


69 002 


69 011 


490 


69 020 


69 028 


69 037 


69 046 


69 055 


69 064 


69 073 


69 082 


69 090 


69 099 


491 


69108 


69117 


69126 


69135 


69144 


69152 


69 161 


69 170 


69179 


69188 


492 


69197 


69 205 


69 214 


69 223 


69 232 


69 241 


69 249 


69 258 


69 267 


69 276 


493 


69 285 


69 294 


69 302 


69 311 


69 320 


69 329 


69 338 


69 346 


69 355 


69 364 


494 


69 373 


69 381 


69 390 


69 399 


69 408 


69 417 


69 425 


69 434 


69 443 


69 452 


495 


69 461 


69 469 


69 478 


69 487 


69 496 


69 504 


69 513 


69 522 


69 531 


69 539 


496 


69 548 


69 557 


69 566 


69 574 


69 583 


69 592 


69 601 


69 609 


69 61S 


69 627 


497 


69 636 


69 644 


69 653 


69 662 


69 671 


69 679 


69 688 


69 697 


69 705 


69 714 


498 


69 723 


69 732 


69 740 


69 749 


69 75S 


69 767 


69 775 


69 784 


69 793 


69 801 


499 


69 810 


69 819 


69 827 


69 836 


69S45 


69 854 


69 862 


69 871 


69 880 


69 88S 


500 


69 897 


69 906 


69 914 


69 923 


69 932 


69 940 


69 949 


69 958 


69 966 


69 975 


S" 





1 


2 


3 


4 


5 


6 


7 


8 


9 



450 - 500 



10 



500-550 



N 


O 


1 


2 


3 4 


5 


6 


7 8 


9 


500 


69 897 


69 906 


69 914 


69 923 69 932 


69 940 


69 949 


69 958 69 966 


69 975 


501 


69 984 


69 992 


70 001 


70 010 70 018 


70 027 


70 036 


70 044 70 053 


70 062 


502 


70 070 


70 079 


70 OSS 


70 096 70105 


70114 


70 122 


70 131 70140 


70148 


.503 


70157 


70 165 


70174 


70183 70191 


70 200 


70 209 


70 217 70 226 


70 234 


504 


70 243 


70 252 


70 260 


70 269 70 278 


70 286 


70 295 


70 303 70 312 


70 321 


505 


70 329 


70 338 


70 346 


70 355 70 364 


70 372 


70 381 


70 389 70 398 


70 406 


506 


70 415 


70 424 


70 432 


70 441 70 449 


70 458 


70 467 


70 475 70 484 


70 492 


"507 


70 501 


70 509 


70 518 


70 526 70 535 


70 544 


70 552 


70 561 70 569 


70 578 


508 


70 586 


70 595 


70 603 


70 612 70 621 


70 629 


70 638 


70 646 70 655 


70 663 


509 


70 672 


70 680 


70 689 


70 697 70 706 


70 714 


70 723 


70 731 70 740 


70 749 


510 


70 757 


70 766 


70 774 


70 783 70 791 


70 800 


70 SOS 


70 817 70 825 


70 834 


511 


70 842 


70 851 


70 859 


70 868 70 876 


70S85 


70 893 


70 902 70 910 


70 919 


512 


70 927 


70 935 


70 944 


70 952 70 961 


70 969 


70 97S 


70 986 70 995 


71003 


513 


71012 


71020 


71029 


71037 71046 


71054 


71063 


71071 71079 


71 OSS 


514 


71096 


71105 


71 113 


71 122 71 130 


71139 


71147 


71 155 71 164 


71172 


515 


71181 


71189 


71198 


71206 71214 


71223 


71231 


71240 7124S 


71257 


516 


71265 


71273 


71282 


71290 71299 


71307 


71315 


71324 71332 


71341 


517 


71349 


71357 


71366 


71374 713S3 


71391 


71399 


71408 71416 


71425 


518 


71433 


71441 


71450 


71458 71466 


71475 


71483 


71492 71500 


7150S 


519 


71517 


71525 


71533 


71542 71550 


71559 


71567 


71575 71584 


71592 


520 


71600 


71609 


71617 


71625 71634 


71642 


71650 


71659 71667 


71675 


521 


71684 


71692 


71700 


71709 71717 


71725 


71734 


71742 71750 


71759 


522 


71767 


71775 


71784 


71792 71800 


71809 


71817 


71825 71834 


71S42 


523 


71850 


71858 


71867 


71875 71883 


71892 


71900 


71908 71917 


71925 


524 


71933 


71941 


71950 


71958 71966 


7197,5 


71983 


71991 71999 


72 008 


525 


72 016 


72 024 


72 032 


72 041 72 049 


72 057 


72 066 


72 074. 72 082 


72 090 


526 


72 099 


72 107 


72115 


72 123 72 132 


72 140 


72 148 


72156 72 165 


72173 


527 


72 181 


72 189 


72 19S 


72 206 72 214 


72 222 


72 230 


72 239 72 247 


72 255 


528 


72 263 


72 272 


72 2S0 


72 28S 72 296 


72 304 


72 313 


72 321 72 329 


72 337 


529 


72 346 


72 354 


72 362 


72 370 72 378 


72 387 


72 395 


72 403 72 411 


72 419 


530 


72 428 


72 436 


72 444 


72 452 72 460 


72 469 


72 477 


72 485 72 493 


72 501 


531 


72 509 


72 51S 


72 526 


72 534 72 542 


72 550 


72 558 


72 567 72 575 


72 583 


532 


72 591 


72 599 


72 607 


72 616 72 624 


72 632 


72 640 


72 648 72 656 


72 665 


533 


72 673 


72 681 


72 689 


72 697 72 7Q5 


72 713 


72 722 


72 730 72 73S 


72 746 


534 


72 754 


72 762 


72 770 


72 779 72 787 


72 795 


72S03 


72 811 72 819 


72 827 


535 


72 835 


72 843 


72 852 


72 860 72 868 


72 876 


72S84 


72 892 72 900 


72 908 


536 


72 916 


72 925 


72 933 


72 941 72 949 


72 957 


72 965 


72 973 72 981 


72 989 


537 


72 997 


73 006 


73 014 


73 022 73 030 


73 038 


73 046 


73 054 73 062 


73 070 


538 


73 078 


73 086 


73 094 


73 102 73 111 


73 119 


73 127 


73 135 73143 


73151 


539 


73159 


73 167 


73 175 


73 183 73 191 


73199 


73 207 


73 215 73 223 


73 231 


540 


73 239 


73 247 


73 255 


73 263 73 272 


73 2S0 


73 28S 


73 296 73 304 


73 312 


541 


73 320 


73 328 


73 336 


73 344 73 352 


73 360 


73 36S 


73 376 73 384 


73 392 


542 


73 400 


73 408 


73 416 


73 424 73 432 


73 440 


73 44S 


73 456 73 464 


73 472 


543 


73 480 


73 488 


73 496 


73 504 73 512 


73 520 


73 528 


73 536 73 544 


73 552 


544 


73 560 


73 568 


73 576 


73 584 73 592 


73 600 


73 608 


73 616 73 624 


73 632 


545 


73 640 


73 648 


73 656 


73 664 73 672 


73 679 


73 687 


73 695 73 703 


73 711 


546 


73 719 


73 727 


73 735 


73 743 73 751 


73 759 


73 767 


73 775 73 783 


73 791 


547 


73 799 


73 807 


73 815 


73S23 73 830 


73 838 


73 846 


73S54 73 862 


73 870 


548 


73S7S 


73 886 


73S94 


73 902 73 910 


73 918 


73 926 


73 933 73 941 


73 949 


549 


73 957 


73 965 


73 973 


73 981 73 9S9 


73 997 


74 005 


74 013 74 020 


74 028 


550 


74 036 


74 044 


74 052 


74 060 74 06S 


74 076 


74 084 


74 092 74 099 


74107 


N 


O 


1 


2 


3 4 


5 


6 


7 8 


9 



500-550 



550-600 



ii 



N 





1 


2 


3 


4 


5 


6 


7 


8 


9 


550 


74 036 


74 044 


74 052 


74 060 


74 068 


74 076 


74 084 


74 092 


74 099 


74 107 


551 


74115 


74 123 


74 131 


74139 


74147 


74155 


74162 


74 170 


74178 


74 186 


552 


74194 


74 202 


74 210 


74 218 


74 225 


74 233 


74 241 


74 249 


74 257 


74 265 


553 


74 273 


74 280 


74 2SS 


74 296 


74 304 


74 312 


74 320 


74 327 


74 335 


74 343 


554 


74 351 


74 359 


74 367 


74 374 


74 382 


74 390 


74 398 


74 406 


74 414 


74 421 


555 


74 429 


74 437 


74 445 


74 453 


74 461 


74 468 


74 476 


74 484 


74 492 


74 500 


556 


74 507 


74 515 


74 523 


74 531 


74 539 


74 547 


74 554 


74 562 


74 570 


74 578 


557 


74 5S6 


74 593 


74 601 


74 609 


74 617 


74 624 


74 632 


74 640 


74 648 


74 656 


558 


74 663 


74 671 


74 679 


74 687 


74 695 


74 702 


74 710 


74 71S 


74 726 


74 733 


559 


74 741 


74 749 


74 757 


74 764 


74 772 


74 780 


74 788 


74 796 


74S03 


74 811 


560 


74 819 


74 827 


74 834 


74S42 


74 850 


74 858 


74 865 


74 873 


74 881 


74 889 


561 


74 896 


74 904 


74 912 


74 920 


74 927 


74 935 


74 943 


74 950 


74 958 


74 966 


562 


74 974 


74 981 


74 989 


74 997 


75 005 


75 012 


75 020 


75 028 


75 035 


75 043 


563 


75 051 


75 059 


75 066 


75 074 


75 0S2 


75 089 


75 097 


75 105 


75 113 


75 120 


564 


75 128 


75 136 


75143 


75 151 


75159 


75 166 


75 174 


75 182 


75 189 


75 197 


565 


75 205 


75 213 


75 220 


75 228 


75 236 


75 243 


75 251 


75 259 


75 266 


75 274 


566 


7-5 282 


75 2S9 


75 297 


75 305 


75 312 


75 320 


75 328 


75 335 


75 343 


75 351 


567 


75 358 


75 366 


75 374 


75 381 


75 3S9 


75 397 


75 404 


75 412 


75 420 


75 427 


568 


75 435 


75 442 


75 450 


75 458 


75 465 


75 473 


75 481 


75 488 


75 496 


75 504 


569 


75 511 


75 519 


75 526 


75 534 


75 542 


75 549 


75 557 


75 565 


75 572 


75 580 


570 


75 587 


75 595 


75 603 


75 610 


75 618 


75 626 


75 633 


75 641 


75 648 


75 656 


571 


75 664 


75 671 


75 679 


75 686 


75 694 


75 702 


75 709 


75 717 


75 724 


75 732 


572 


75 740 


75 747 


75 755 


75 762 


75 770 


75 778 


75 785 


75 793 


75 800 


75 SOS 


573 


75 815 


75 823 


75 831 


75 838 


75 846 


75 853 


75S61 


75 868 


75 876 


75 884 


574 


75 891 


75 899 


75 906 


75 914 


75 921 


75 929 


75 937 


75 944 


75 952 


75 959 


575" 


75 967 


75 974 


75 982 


75 989 


75 997 


76 005 


76 012 


76 020 


76 027 


76 035 


576 


76 042 


76 050 


76 057 


76 065 


76 072 


76 080 


76 087 


76 095 


76103 


76110 


577 


76 US 


76125 


76133 


76140 


76148 


76155 


76163 


76170 


76178 


76185 


• 578 


76193 


76 200 


76 20S 


76 215 


76 223 


76 230 


76 238 


76 245 


76 253 


76 260 


579 


76 26S 


76 275 


76 283 


76 290 


76 298 


76 305 


76 313 


76 320 


76 328 


76 335 


580 


- 76 343 


76 350 


76 358 


76 365 


76 373 


76 380 


76 388 


76 395 


76403 


76 410 


581 


76 418 


76 425 


76 433 


76 440 


76 448 


76 455 


76 462 


76 470 


76 477 


76 485 


582 


76 492 


76 500 


76 507 


76 515 


76 522 


76 530 


76 537 


76 545 


76 552 


76 559 


583 


76 567 


76 574 


76 5S2 


76 589 


76 597 


76 604 


76 612 


76 619 


76 626 


76 634 


584 


76 641 


76 649 


76 656 


76 664 


76 671 


76 678 


76 686 


76 693 


76 701 


76 70S 


585 


76 716 


76 723 


76 730 


76 738 


76 745 


76 753 


76 760 


76 768 


76 775 


76 782 


586 


76 790 


76 797 


76 805 


76 812 


76 819 


76 827 


76 834 


76 842 


76 849 


76 856 


587 


76 864 


76S71 


76 879 


76 8S6 


76S93 


76 901 


76 908 


76 916 


76 923 


76 930 


588 


76 938 


76 945 


76 953 


76 960 


76 967 


76 975 


76 9S2 


76 989 


76 997 


77 004 


589 


77 012 


77 019 


77 026 


77 034 


77 041 


77 048 


77 056 


77 063 


77 070 


77 078 


590 


77 085 


77 093 


77100 


77107 


77115 


77122 


77129 


77137 


77144 


77151 


591 


77159 


77166 


77173 


77181 


77188 


77195 


77 203 


77 210 


77 217 


77 225 


592 


77 232 


77 240 


77 247 


77 254 


77 262 


77 269 


77 276 


77 283 


77 291 


77 298 


593 


77 305 


77 313 


77 320 


77 327 


77 335 


77 342 


77 349 


77 357 


77 364 


77 371 


594 


77 379 


77 386 


77 393 


77 401 


77 408 


77 415 


77 422 


77 430 


77 437 


77 444 


595 


77 452 


77 459 


77 466 


77 474 


77 481 


77 488 


77 495 


77 503 


77 510 


77 517 


596 


77 525 


77 532 


77 539 


77 546 


77 554 


77 561 


77 568 


77 576 


77 583 


77 590 


597 


77 597 


77 605 


77 612 


77 619 


77 627 


77 634 


77 641 


77 64S 


77 656 


77 663 


598 


77 670 


77 677 


77 685 


77 692 


77 699 


77 706 


77 714 


77 721 


77 728 


77 735 


599 


77 743 


77 750 


77 757 


77 764 


77 772 


77 779 


77 7S6 


77 793 


77 801 


77 808 


600 


77 815 


77 822 


77 830 


77 837 


77 844 


77 851 


77 859 


77 866 


77 873 


77 8SO 


N 





1 


2 


3 


4 


5 


6 


7 


8 


9 



550-600 



12 



600-650 



N 





1 


2 


3 4 


5 

77 851 


6 


7 


8 


9 


600 


77 815 


77 822 


77 830 


77 837 77 844 


77 859 


77 866 


77 873 


77 880 


601 


77 887 


77 895 


77 902 


77 909 77 916 


77 924 


77 931 


77 938 


77 945 


77 952 


602 


77 960 


77 967 


77 974 


77 981 77 988 


77 996 


78 003 


78 010 


78 017 


78 025 


603 


78 032 


78 039 


78 046 


78 053 78 061 


78 068 


78 075 


78 082 


78 0S9 


78 097 


'604 


78104 


78111 


78118 


78125 78132 


78140 


78147 


78154 


78161 


78168 


605 


78176 


78183 


78190 


78197 78 204 


78 211 


78 219 


78 226 


78 233 


78 240 


606 


78 247 


78 254 


78 262 


78 269 78 276 


78 283 


78 290 


78 297 


78 305 


78 312 


607 


78 319 


78 326 


78 333 


78 340 78 347 


78 355 


78 362 


78 369 


78 376 


78 383 


608 


78 390 


78 398 


78 405 


78 412 78 419 


78 426 


78 433 


78 440 


78 447 


78 455 


609 


78 462 


78 469 


78 476 


78 483 78 490 


78 497 


78 504 


78 512 


78 519 


78 526 


610 


78 533 


78 540 


78 547 


78 554 78 561 


78 569 


78 576 


78 583 


78 590 


78 597 


611 


78 604 


78 611 


78 618 


78 625 78 633 


78 640 


78 647 


78 654 


78 661 


78 668 


612 


78 675 


78 682 


78 689 


78 696 78 704 


78 711 


78 718 


78 725 


78 732 


78 739 


613 


78 746 


78 753 


78 760 


78 767 78 774 


78 781 


78 789 


78 796 


78 803 


78 810 


614 


78 817 


78 824 


78 831 


78 838 78 845 


78 852 


78 859 


78 866 


78 873 


78 880 


615 


78 888 


78 895 


78 902 


78 909 78 916 


78 923 


78 930 


78 937 


78 944 


78 951 


. 616 


78 958 


7S965 


78 972 


78 979 78 986 


78 993 


79 000 


79 007 


79 014 


79 021 


617 


79 029 


79 036 


79 043 


79 050 79 057 


79 064 


79 071 


79 078 


79 085 


79 092 


618 


79 099 


79 106 


79113 


79120 79127 


79134 


79141 


79148 


79155 


79162 


619 


79169 


79176 


79183 


79190 79197 


79 204 


79 211 


79 218 


79 225 


79 232 


620 


79 239 


79 246 


79 253 


79 260 79 267 


79 274 


79 281 


79 288 


79 295 


79 302 


621 


79 309 


79 316 


79 323 


79 330 79 337 


79 344 


79 351 


79 358 


79 365 


79 372 


622 


79 379 


79 386 


79 393 


79 400 79 407 


79 414 


79 421 


79 428 


79 435 


79 442 


623 


79 449 


79 456 


79 463 


79 470 79 477 


79 484 


79 491 


79 498 


79 505 


79 511 


624 


79 518 


79 525 


79 532 


79 539 79 546 


79 553 


79 560 


79 567 


79 574 


79 581 


625 


79 588 


79 595 


79 602 


79 609 79 616 


79 623 


79 63.0 


79 637 


79 644 


79 650 


626 


79 657 


79 664 


79 671 


79 678 79 685 


79 692 


79 699 


79 706 


79 713 


79 720 


627 


79 727 


79 734 


79 741 


79 748 79 754 


79 761 


79 768 


79 775 


79 782 


79 789 


628 


79 796 


79 803 


79 810 


79 817 79 824 


79 831 


79 837 


79 844 


79 851 


79 858 


629 


79 865 


79 872 


79 879 


79 8S6 79 893 


79 900 


79 906 


79 913 


79 920 


79 927 


630 


79 934 


79 941 


79 948 


79 955 79 962 


79 969 


79 975 


79 982 


79 9S9 


79 996 


631 


80 003 


80 010 


80 017 


SO 024 80 030 


80 037 


80 044 


80 051 


80 058 


80 065 


632 


80 072 


80 079 


80 085 


80 092 80 099 


80106 


80113 


80120 


80127 


80 134 


633 


80140 


80 147 


80154 


80161 80168 


80175 


80182 


801SS 


SO 195 


80 202 


634 


80 209 


80 216 


80 223 


80 229 80 236 


80 243 


80 250 


80 257 


80 264 


80 271 


635 


80 277 


80 284 


80 291 


80 298 80 305 


80 312 


80 318 


80 325 


80 332 


80 339 


636 


80 346 


80 353 


80 359 


80 366 80 373 


SO 380 


80 387 


80 393 


80 400 


80 407 


637 


80 414 


80 421 


80 428 


80 434 80 441 


80 448 


80 455 


80 462 


80 468 


80 475 


638 


80 482 


80 489 


80 496 


80 502 80 509 


80 516 


80 523 


80 530 


80 536 


80 543 


639 


80 550 


80 557 


80 564 


80 570 80 577 


80 584 


SO 591 


80 598 


80 604 


80 611 


640 


80 618 


80 625 


80 632 


80 638 80 645 


80 652 


80 659 


80 665 


80 672 


80 679 


641 


80 686 


80 693 


80 699 


80 706 80 713 


80 720 


80 726 


80 733 


80 740 


80 747 


642 


80 754 


80 760 


80 767 


80 774 80 781 


80 787 


80 794 


80 SOI 


SO 808 


80 814 


643 


80 821 


80 828 


80 835 


80 841 80 848 


80 855 


80 862 


80 868 


80 875 


S0 8S2 


644 


80 889 


80 895 


80 902 


80 909 80 916 


80 922 


80 929 


80 936 


80 943 


80 949 


645 


80 956 


80 963 


80 969 


80 976*80 983 


80 990 


80 996 


81003 


81010 


SI 017 


646 


81023 


81030 


81037 


81043 81050 


81057 


81064 


81070 


81077 


81084 


647 


81090 


81097 


81104 


81 111 81 117 


81124 


81131 


81137 


81144 


81151 


648 


81158 


81164 


81171 


81178 81184 


81191 


S119S 


81204 


81211 


81218 


649 


81224 


81231 


81238 


81245 81251 


81258 


81265 


81271 


81278 


81285 


650 


81291 


81298 
1 


81305 


81311 SI 318 


81325 


81331 


81338 


81345 


81351 


X 





2 


3 . 4 


5 


6 


7 


8 


9 



600-650 



650-700 



13 



N 





1 


2 


3 


4 


5 


6 7 


8 


9 


650 


SI 291 


S129S 


81305 


SI 311 


81318 


81325 


81331 81338 


81345 


81351 


651 


S135S 


SI 365 


81 371 


SI 378 


SI 385 


81391 


81 398-81 405 


81411 


81418 


652 


81425 


SI 431 


SI 438 


81445 


SI 451 


S145S 


SI 465 81471 


81478 


814S5 


653 


81491 


8149S 


SI 505 


81511 


81518 


81525 


81531 SI 538 


81544 


81551 


654 


81558 


SI 564 


SI 571 


S157S 


81 5S4 


81591 


8159S SI 604 


81611 


81617 


655 


81624 


SI 631 


81637 


81644 


81 651 


81657 


81664 81671 


81677 


81684 


656 


81690 


SI 697 


81704 


81710 


81717 


81723 


81730 81737 


81743 


81750 


657 


81757 


SI 763 


81770 


81776 


817S3 


81790 


81796 81 803 


81809 


81816 


• 658 


81823 


81829 


81836 


81842 


81849 


81856 


81862 81869 


81875 


81882 


659 


SI 889 


81895 


81902 


81908 


81915 


81921 


81928 81935 


81941 


81948 


660 


81954 


81961 


81968 


81974 


81981 


81987 


SI 994 82 000 


82 007 


82 014 


661 


82 020 


S2 027 


82 033 


82 040 


82 046 


82 053 


82 060 82 066 


82 073 


82 079 


662 


82 086 


82 092 


82 099 


82105 


82112 


82119 


82125 82132 


82138 


82145 


663 


82 151 


82 15S 


82164 


82 171 


82 17S 


82184 


82 191 82197 


82 204 


82 210 


664 


82 217 


82 223 


82 230 


82 236 


82 243 


82 249 


82 256 82 263 


82 269 


82 276 


665 


82 282 


82 289 


82 295 


82 302 


82 308 


82 315 


82 321 82-328 


82 334 


82 341 


666 


-82 347 


82 354 


82 360 


82 367 


82 373 


82 380 


82 387 82 393 


82 400 


82 406 


667 


82 413 


82 419 


82 426 


82 432 


82 439 


82 445 


82 452 82 458 


82 465 


82 471 


668 


82 478 


82 484 


82 491 


82 497 


82 504 


82 510 


82 517 82 523 


82 530 


82 536 


669 


82 543 


82 549 


82 556 


82 562 


82 569 


82 575 


82 582 82 588 


82 595 


82 601 


670 


82 607 


82 614 


82 620 


82 627 


82 633 


82 640 


82 646 82 653 


82 659 


82 666 


671 


82 672 


82 679 


S2 6S5 


82 692 


82 698 


82 705 


82 711 82 718 


82 724 


82 730 


672 


82 737 


82 743 


82 750 


82 756 


82 763 


82 769 


82 776 82 782 


82 789 


82 795 


673 


82 802 


82 SOS 


82 814 


82 821 


82 827 


82 834 


82 840 82 847 


82 853 


82 860 


' 674 


82 866 


82 872 


82 879 


82 885 


82 892 


82 898 


82 905 82 911 


82 918 


82 924 


675 


82 930 


82 937 


82 943 


82 950 


82 956 


82 963 


82 969 82 975 


82 982 


82 988 


676 


82 995 


83 001 


83 008 


83 014 


83 020 


83 027 


83 033 83 040 


83 046 


83 052 


677 


83 059 


83 065 


83 072 


83 078 


83 0S5 


83 091 


83 097 83 104 


83110 


83 117 


678 


83 123 


83 129 


83 136 


83 142 


83149 


83 155 


83 161 83 168 


83174 


83 181 


679 


83187 


83 193 


83 200 


83 206 


83 213 


83 219 


83 225 83 232 


83 238 


83 245 


680 


83 251 


S3 257 


83 264 


83 270 


83 276 


83 283 


83 2S9 83 296 


83 302 


83 308 


681 


83 315 


83 321 


83 327 


83 334 


83 340 


83 347 


83 353 83 359 


83 366 


83 372 


682 


83 378 


S3 3S5 


83 391 


83 398 


83 404 


83 410 


83 417 83 423 


83 429 


83 436 


683 


83 442 


83 448 


83 455 


83 461 


83 467 


83 474 


83 480 83 487 


83 493 


83 499 


684 


83 506 


83 512 


S3 51S 


83 525 


83 531 


83 537 


83 544 83 550 


83 556 


83 563 


685 


83 569 


83 575 


83 582 


83 588 


83 594 


83 601 


83 607 83 613 


83 620 


83 626 


686 


83 632 


83 639 


83 645 


83 651 


S3 658 


83 664 


83 670 83 677 


83 683 


83 689 


687 


83 696 


S3 702 


S3 708 


83 715 


83 721 


83 727 


83 734 83 740 


83 746 


83 753 


688 


83 759 


83 765 


83 771 


83 778 


83 784 


83 790 


83 797 83 803 


83S09 


83 816 


689 


83 822 


83 828 


83 835 


83 841 


83 847 


83 853 


83 860 83 866 


83 872 


83 879 


690 


83 885 


83 891 


83 897 


83 904 


83 910 


83 916 


83 923 83 929 


83 935 


83 942 


691 


83 948 


83 954 


83 960 


83 967 


83 973 


83 979 


S3 9S5 83 992 


83 998 


84 004 


692 


84 011 


84 017 


84 023 


84 029 


84 036 


84 042 


84 048 84 055 


84 061 


84 067 


693 


84 073 


84 080 


84 0S6 


84 092 


84 09S 


84 105 


84111 84 117 


84123 


84130 


694 


84 136 


84142 


84148 


84155 


84 161 


84 167 


84173 84 ISO 


S41S6 


84192 


695 


84198 


84 205 


84 211 


84 217 


84 223 


84 230 


84 236 84 242 


84 248 


84 255 


696 


84 261 


84 267 


84 273 


84 280 


S4 2S6 


84 292 


84 298 84 305 


84 311 


84 317 


697 


84 323 


84 330 


84 336 


84 342 


84 34S 


84 354 


84 361 84 367 


84 373 


84 379 


698 


84 386 


84 392 


84 39S 


84 404 


84 410 


84 417 


84 423 84 429 


S4 435 


84 442 


699 


84 448 


84 454 


84 460 


84 466 


84 473 


84 479 


84 485 84491 


84 497 


84 504 


700 


S4 510 


84 516 


84 522 


S4 528 


84 535 


84 541 


84 547 84 553 


84 559 


84 566 


N 





1 


2 


3 


4 


5 


6 7 


8 


9 



650-700 



14 








700-750 










N 





1 


2 


3 4 


5 

84 541 


6 


7 


8 


9 


700 


84 510 


84 516 


84 522 


84 528 84 535 


84 547 


84 553 


84 559 


84 566 


701 


84 572 


84 578 


84 584 


84 590 84 597 


84 603 


84 609 


84 615 


84 621 


84 628 


702 


84 634 


84 640 


84 646 


84 652 84 658 


84 665 


84 671 


S4 677 


84 683 


84 689 


703 


84 696 


84 702 


S4 708 


84 714 84 720 


84 726 


84 733 


84 739 


84 745 


84 751 


704 


84 757 


84 763 


84 770 


84 776 84 782 


84 788 


84 794 


84 800 


84 807 


84 813 


705 


84 819 


84 825 


84 831 


84 837 84 844 


84 850 


84 856 


84 862 


84 868 


84 874 


706 


84 880 


84 887 


84 893 


84 899 84 905 


84 911 


84 917 


84 924 


84 930 


84 936 


707 


84 942 


84 948 


84 954 


84 960 84 967 


84 973 


84 979 


84 985 


84 991 


84 997 


708 


85 003 


85 009 


85 016 


85 022 85 028 


85 034 


85 040 


85 046 


85 052 


85 058 


709 


85 065 


85 071 


85 077 


85 083 85 089 


85 095 


85 101 


85 107 


85 114 


85 120 


710 


85 126 


85132 


85 138 


85 144 85 150 


85156 


85 163 


85 169 


85175 


85181 


711 


85 187 


85 193 


85 199 


85 205 85 211 


85 217 


85 224 


85 230 


85 236 


85 242 


712 


85 248 


85 254 


85 260 


85 266 85 272 


85 278 


85 285 


85 291 


85 297 


85 303 


713 


85 309 


85 315 


85 321 


85 327 85 333 


85 339 


85 345 


85 352 


85 358 


85 364 


714 


. 85 370 


85 376 


S5 382 


85 388 85 394 


85 400 


85 406 


85 412 


85 418 


85 425 


715 


85 431 


85 437 


85 443 


85 449 85 455 


85 461 


85 467 


85 473 


85 479 


85 485 


716 


85 491 


85 497 


85 503 


85 509 85 516 


85 522 


85 528 


85 534 


85 540 


85 546 


717 


85 552 


85 558 


85 564 


85 570 85 576 


S5 582 


85 588 


85 594 


85 600 


85 606 


718 


85 612 


85 618 


85 625 


85 631 85 637 


85 643 


85 649 


85 655 


85 661 


85 667 


719 


85 673 


85 679 


85 685 


85 691 85 697 


85 703 


85 709 


85 715 


85 721 


85 727 


720 


85 733 


85 739 


85 745 


85 751 85 757 


85 763 


85 769 


85 775 


85 781 


85 788 


721 


85 794 


85 800 


85 806 


85 812 85 818 


85 824 


85 830 


85 836 


85 842 


85 848 


722 


85 854 


85 860 


85 866 


85 872 85 878 


85 884 


85 890 


85 896 


85 902 


85 908 


723 


85 914 


85 920 


85 926 


85 932 85 938 


85 944 


85 950 


85 956 


85 962 


85 968 


724 


85 974 


85 980 


85 986 


85 992 85 998 


86 004 


86 010 


86 016 


86 022 


86 028 


725 


86 034 


86 040 


86 046 


86 052 S6 058 


86 064 


86 070 


86 076 


86 082 


86 088 


726 


86 094 


86100 


86106 


86112 86118 


86124 


86130 


86136 


86141 


86147 


727 


86153 


86159 


86165 


86171 86177 


86183 


86189 


86195 


86 201 


S6 207 


728 


86 213 


86 219 


86 225 


86 231 86 237 


86 243 


86 249 


86 255 


86 261 


86 267 


729 


86 273 


86 279 


86 285 


86 291 86 297 


86 303 


86 308 


86 314 


86 320 


86 326 


730 


86 332 


86 338 


86 344 


86 350 86 356 


86 362 


86 368 


86 374 


86 380 


86 386 


731 


86 392 


86 398 


86 404 


86 410 86 415 


86 421 


86 427 


86 433 


86 439 


86 445 


732 


86 451 


86 457 


86 463 


86 469 86 475 


86 4S1 


86 487 


86 493 


S6 499 


86 504 


733 


86 510 


86 516 


86 522 


86 528 86 534 


86 540 


86 546 


86 552 


86 558 


86 564 


734 


86 570 


86 576 


86 581 


86 587 86 593 


86 599 


86 605 


86 611 


86 617 


86 623 


735 


86 629 


86 635 


86 641 


86 646 86 652 


86 658 


86 664 


86 670 


86 676 


86 682 


736 


86 688 


86 694 


86 700 


86 705 86 711 


86 717 


86 723 


86 729 


86 735 


86 741 


737 


86 747 


86 753 


86 759 


86 764 86 770 


86 776 


86 782 


86 788 


86 794 


86 800 


738 


86 806 


86 812 


86 817 


86 823 86 829 


86 835 


86 841 


86 847 


86 853 


86 859 


739 


86 864 


86 870 


86 876 


86 882 86 888 


86 894 


86 900 


86 906 


86 911 


86 917 


740 


86 923 


86 929 


86 935 


86 941 86 947 


86 953 


86 958 


86 964 


86 970 


86 976 


741 


86 982 


86 98S 


S6 994 


86 999 87 005 


87 011 


87 017 


87 023 


87 029 


87 035 


742 


87 040 


87 046 


87 052 


87 058 87 064 


87 070 


87 075 


S7 0S1 


87 087 


87 093 


743 


87 099 


87105 


87111 


87116 87122 


87128 


S7134 


87 140 


87146 


87151 


744 


87157 


87163 


87169 


87175 87181 


871S6 


87192 


87198 


87 204 


87 210 


745 


87 216 


87 221 


87 227 


87 233" 87 239 


87 245 


87 251 


87 256 


87 262 


87 268 


746 


87 274 


87 280 


87 286 


87 291 87 297 


87 303 


87 309 


87 315 


87 320 


87 326 


747 


87 332 


87 338 


87 344 


87 349 87 355 


87 361 


87 367 


87 373 


87 379 


87 384 


748 


87 390 


87 396 


87 402 


87 40S 87 413 


87 419 


87 425 


87 431 


87 437 


87 442 


749 


87 448 


87 454 


87 460 


87 466 S7 471 


87 477 


87 483 


87 489 


87 495 


87 500 


750 


87 506 


87 512 


87 518 


87 523 87 529 


87 535 


87 541 


87 547 


87 552 


87 558 


N 


O 


1 


2 


3. 4 


5 


6 


7 


8 


9 



700 -7S0 



750-800 



15 



X 





1 


2 


3 


4 


5 


6 


7 


8 


9 


750 


87 506 


87 512 


87 5 IS 


87 523 


87 529 


S7 535 


S7 541 


87 547 


87 552 


87 558 


751 


87 564 


87 570 


87 576 


87 581 


87 587 


87 593 


87 599 


87 604 


87 610 


87 616 


752 


87 622 


87 628 


87 633 


S7 639 


87 645 


S7 651 


87 656 


87 662 


S7 668 


87 674 


753 


87 679 


S7 6S5 


87 691 


87 697 


87 703 


87 70S 


87 714 


87 720 


87 726 


87 731 


754 


87 737 


87 743 


87 749 


87 754 


87 760 


87 766 


87 772 


87 777 


87 783 


87 789 


755 


87 795 


87 800 


87 806 


87 812 


87 SIS 


87 823 


87 829 


87 835 


87 841 


87 846 


756 


87S52 


S7S58 


87 864 


87 869 


87S75 


87 SSI 


87 8S7 


87 892 


87 898 


87 904 


757 


87 910 


87 915 


87 921 


87 927 


87 933 


87 938 


87 944 


87 950 


87 955 


87 961 


758 


87 967 


S7 973 


87 978 


87 9S4 


87 990 


87 996 


8S001 


88 007 


8S013 


88 018 


759 


88 024 


88 030 


88 036 


88 041 


8S047 


88 053 


88 058 


88 064 


88 070 


88 076 


760 


88 081 


88 087 


88 093 


SS09S 


88104 


88 110 


88116 


88121 


88127 


88133 


761 


88138 


88144 


88 150 


8S156 


88161 


88167 


88173 


88178 


88 184 


8S190 


762 


88 195 


SS201 


88 207 


88 213 


88 218 


88 224 


88 230 


88 235 


88 241 


88 247 


763 


88 252 


88 258 


88 264 


88 270 


88 275 


88 281 


88 287 


88 292 


88 298 


88 304 


764 


88 309 


88 315 


88 321 


88 326 


88 332 


88 338 


88 343 


88 349 


88 355 


88 360 


765 


88 366 


88 372 


88 377 


S8 383 


88 389 


88 395 


88 400 


88 406 


88 412 


88 417 


766 


88 423 


88 429 


88 434 


88 440 


88 446 


88 451 


88 457 


88 463 


88 468 


88 474 


767 


88 480 


S8 485 


88 491 


88 497 


88 502 


88 508 


88 513 


88 519 


88 525 


88 530 


76S 


88 536 


88 542 


8S547 


88 553 


88 559 


88 564 


88 570 


88 576 


88 581 


88 587 


769 


88 593 


88 598 


88 604 


88 610 


88 615 


S8 621 


88 627 


88 632 


88 638 


8S643 


770 


88 649 


88 655 


88 660 


88 666 


88 672 


88 677 


88 683 


8S6S9 


88 694 


88 700 


771 


88 705 


88 711 


88 717 


88 722 


88 728 


88 734 


88 739 


88 745 


88 750 


88 756 


772 


88 762 


88 767 


88 773 


88 779 


88 784 


88 790 


88 795 


88 801 


88 807 


88 812 


773 


88 818 


88 824 


8S829 


88 835 


88 840 


88 846 


88 852 


88 857 


88 863 


88 868 


774 


88 874 


S8 8S0 


88 885 


88 891 


8SS97 


88 902 


88 908 


88 913 


88 919 


88 925 


775 


88 930 


88 936 


88 941 


88 947 


8S953 


88 958 


88 964 


88 969 


88 975 


88 981 


776 


88 986 


88 992 


88 997 


89 003 


89 009 


89 014 


89 020 


89 025 


89 031 


89 037 


777 


89 042 


89 048 


89 053 


89 059 


89 064 


89 070 


89 076 


89 081 


89 087 


89 092 


773 


89 098 


89104 


89 109 


89 115 


89120 


89126 


89 131 


89 137 


89143 


89148 


779 


89154 


89159 


89165 


89170 


89176 


89182 


89187 


89193 


89198 


89 204 


780" 


89 209 


89 215 


89 221 


89 226 


89 232 


89 237 


89 243 


89 248 


89 254 


89 260 


781 


89 265 


89 271 


'89 276 


89 282 


89 287 


89 293 


89 298 


89 304 


89 310 


89 315 


782 


89 321 


89 326 


89 332 


89 337 


89 343 


89 348 


89 354 


89 360 


89 365 


89 371. - 


783 


89 376 


89 382 


89 387 


89 393 


89 398 


89 404 


89 409 


89 415 


89 421 


89 426 


784 


89 432 


89 437 


89 443 


89 448 


89 454 


89 459 


89 465 


89 470 


89 476 


89 481 


785 


89 487 


89 492 


89 498 


89 504 


89 509 


89 515 


89 520 


89 526 


89 531 


89 537 


786 


89 542 


89 548 


89 553 


89 559 


89 564 


89 570 


89 575 


89 581 


89 586 


89 592 


787 


89 597 


89 603 


89 609 


89 614 


89 620 


89 62i 


89 631 


89 636 


89 642 


89 647 


788 


89 653 


89 658 


89 664 


89 669 


89 675 


89 680 


89 686 


89 691 


89 697 


89 702 


789 


89 708 


89 713 


89 719 


89 724 


89 730 


89 735 


89 741 


89 746 


89 752 


89 757 


790 


89 763 


89 768 


89 774 


89 779 


89 785 


89 790 


89 796 


89 801 


89 807 


89 812 


791 


89 818 


89 823 


89 829 


89 834 


89S40 


89 845 


89 851 


89 856 


89 862 


89 867 


792 


89S73 


89 878 


89 883 


89 8S9 


89 894 


89 900 


89 905 


89 911 


89 916 


89 922 


793 


89 927 


89 933 


89 938 


89 944 


89 949 


89 955 


89 960 


89 966 


89 971 


89 977 


794 


89 982 


89 988 


89 993 


89 998 


90 004 


90 009 


90 015 


90 020 


90 026 


90 031 


795 


90 037 


90 042 


90 048 


90 053 


90 059 


90 064 


90 069 


90 075 


90 080 


90 086 


796 


90 091 


90 097 


90 102 


90 108 


90113 


90119 


90124 


90 129 


90135 


90140 


797 


90146 


90151 


90157 


90162 


9016S 


90173 


90179 


90184 


90189 


90195 


798 


90 200 


90 206 


90 211 


90 217 


90 222 


90 227 


90 233 


90 238 


90 244 


90 249 


799 


90 255 


90 260 


90 266 


90 271 


90 276 


90 282 


90 287 


90 293 


90 298 


90 304 


800 


90 309 


90 314 


90 320 


90 325 


90 331 


90 336 


90 342 


90 347 


90 352 


90 358 


N 


O 


1 


2 


3 


4 


5 


6 


7 


8 


9 



750-800 



16 








800-850 










N 


O 


1 


2 


3 


4 


5 


6 


7 


8 


9 


800 


90 309 


90 314 


90 320 


90 325 


90 331 


90 336 


90 342 


90 347 


90 352 


90 358 


801 


90 363 


90 369 


90 374 


90 380 


90 385 


90 390 


90 396 


90 401 


90 407 


90 412 


802 


90 417 


90 423 


90 428 


90 434 


90 439 


90 445 


90 450 


90 455 


90 461 


90 466 


803 


90 472 


90 477 


90 482 


90 488 


90 493 


90 499 


90 504 


90 509 


90 515 


90 520 


804 


90 526 


90 531 


90 536 


90 542 


90 547 


90 553 


90 558 


90 563 


90 569 


90 574 


805 


90 580 


90 585 


90 590 


90 596 


90 601 


90 607 


90 612 


90 617 


90 623 


90 628 


806 


90 634 


90 639 


90 644 


90 650 


90 655 


90 660 


90 666 


90 671 


90 677 


90 682 


807 


90 687 


90 693 


90 698 


90 703 


90 709 


90 714 


90 720 


90 725 


90 730 


90 736 


808 


90 741 


90 747 


90 752 


90 757 


90 763 


90 768 


90 773 


90 779 


90 784 


90 789 


809 


90 795 


90 800 


90 806 


90 811 


90 816 


90 822 


90 827 


90 832 


90 838 


90 843 


810 


90 849 


90 854 


90 859 


90 865 


90 870 


90 875 


90 881 


90 886 


90 891 


90 897 


811 


90 902 


90 907 


90913 


90 918 


90 924 


90 929 


90 934 


90 940 


90 945 


90 950 


812 


90 956 


90 961 


90 966 


90 972 


90 977 


90 982 


90 988 


90 993 


90 998 


91004 


813 


91009 


91014 


91020 


91025 


91030 


91036 


91041 


91046 


91052 


91057 


814 


91 062 


91068 


91073 


91078 


91084 


91089 


91094 


91100 


91105 


91110 


815 


91 116 


91121 


91126 


91132 


91137 


91142 


91148 


91153 


91158 


91164 


816 


91169 


91174 


91180 


91185 


91190 


91196 


91201 


91206 


91212 


91217 


817 


91222 


91228 


91233 


91238 


91243 


91249 


91254 


91259 


91265 


91270 


818 


91275 


912S1 


91286 


91291 


91297 


91302 


91307 


91312 


91318 


91323 


819 


91328 


91334 


91339 


91344 


91350 


91355 


91360 


91365 


91371 


91376 


820 


91381 


91387 


91392 


91397 


91403 


91408 


91413 


91418 


91424 


91429 


821 


91434 


91440 


91445 


91450 


91455 


91461 


91466 


91471 


91477 


91482 


822 


91487 


91492 


91498 


91503 


91508 


91514 


91519 


91524 


91529 


91535 


823 


91540 


91545 


91551 


91556 


91561 


91566 


91572 


91577 


91582 


91587 


824 


91593 


91598 


91603 


91609 


91614 


91 61^ 91 624 


91630 


91635 


91640 


825 


91645 


91651 


91656 


91661 


91666 


91 672 


91677 


91682 


91687 


91693 


826 


9169S 


91703 


91709 


91714 


91719 


91724 


91730 


91735 


91740 


91745 


827 


91751 


91756 


91761 


91766 


91772 


91777 


91782 


91787 


91793 


91798 


828 


91803 


91808 


91814 


91819 


91824 


91829 


91834 


91840 


91845 


91850 


829 


91855 


91861 


91866 


91871 


91876 


91882 


91 887 


91892 


91897 


91903 


830 


91908 


91913 


91918 


91924 


91929 


91934 


91939 


91944 


91950 


91955 


831 


91960 


91965 


91971 


91976 


91981 


91986 


91991 


91997 


92 002 


92 007 


832 


92 012 


92 018 


92 023 


92 028 


92 033 


92 038 


92 044 


92 049 


92 054 


92 059 


833 


92 065 


92 070 


92 075 


92 080 


92 085. 


92 091 


92 096 


92 101 


92 106 


92111 


834 


92 117 


92 122 


92 127 


92132 


92137 


92 143 


92 148 


92 153 


92158 


92 163 


835 


92169 


92174 


92179 


92184 


92189 


92195 


92 200 


92 205 


92 210 


92 215 


836 


92 221 


92 226 


92 231 


92 236 


92 241 


92 247 


92 252 


92 257 


92 262 


92 267 


837 


92 273 


92 278 


92 283 


92 288 


92 293 


92 298 


92 304 


92 309 


92 314 


92 319 


838 


92 324 


92 330 


92 335 


92 340 


92 345 


92 350 


92 355 


92 361 


92 366 


92 371 


839 


92 376 


92 381 


92 387 


92 .392 


92 397 


92 402 


92 407 


92 412 


92 418 


92 423 


840 


92 428 


92 433 


92 438 


92 443 


92 449 


92 454 


92 459 


92 464 


92 469 


92 474 


841 


92 480 


92 485 


92 490 


92 495 


92 500 


92 505 


92 511 


92 516 


92 521 


92 526 


842 


92 531 


92 536 


92 542 


92 547 


92 552 


92 557 


92 562 


92 567 


92 572 


92 578 


843 


92 583 


92 588 


92 593 


92 598 


92 603 


92 609 


92 614 


92 619 


92 624 


92 629 


844 


92 634 


92 639 


92 645 


92 650 


92 655 


92 660 


92 665 


92 670 


92 675 


92 681 


845 


92 686 


92 691 


92 696 


92 701 


92 706 


92 711 


92 716 


92 722 


92 727 


92 732 


846 


92 737 


92 742 


92 747 


92 752 


92 758 


92 763 


92 768 


92 773 


92 778 


92 783 


847 


92 788 


92 793 


92 799 


92 804 


92 809 


92S14 


92 819 


92 824 


92 829 


92 834 


848 


92 840 


92 845 


92 850 


92 855 


92S60 


92 865 


92 870 


92 875 


92 881 


92 886 


849 


92 891 


92 896 


92 901 


92 906 


92 911 


92 916 


92 921 


92 927 


92 932 


92 937 


850 


92 942 


92 947 


92 952 


92 957 


92 962 


92 967 


92 973 


92 978 


92 983 


92 988 


N 


O 


1 


2 


3 


- 4 


5 


6 


7 


8 


9 



800-850 











850-900 








17 


N 





1 


2 


3 


4 


5 


6 


7 


8 


9 


850 


92 942 


92 947 


92 952 


92 957 


92 962 


92 967 


92 973 


92 978 


92 983 


92 988 


851 


92 993 


92 998 


93 003 


93 008 


93 013 


93 018 


93 024 


93 029 


93 034 


93 039 


852 


93 044 


93 049 


93 054 


93 059 


93 064 


93 069 


93 075 


93 080 


93 085 


93 090 


853 


93 095 


93 100 


93 105 


93 110 


93 115 


93 120 


93 125 


93 131 


93 136 


93141 


854 


93 146 


93 151 


93 156 


93161 


93 166 


93 171 


93 176 


93 181 


93 186 


93192 


855 


93197 


93 202 


93 207 


93 212 


93 217 


93 222 


93 227 


93 232 


93 237 


93 242 


.856 


93 247 


93 252 


93 258 


93 263 


93 268 


93 273 


93 278 


93 283 


93 288 


93 293 


857 


93 298 


93 303 


93 30S 


93 313 


93 318 


93 323 


93 328 


93 334 


93 339 


93 344 


858 


93 349 


93 354 


93 359 


93 364 


93 369 


93 374 


93 379 


93 384 


93 389 


93 394 


859 


93 399 


93 404 


93 409 


93 414 


93 420 


93 425 


93 430 


93 435 


93 440 


93 445 


860 


93 450 


93 455 


93 460 


93 465 


93 470 


93 475 


93 480 


93 485 


93 490 


93 495 


861 


93 500 


93 505 


93 510 


93 515 


93 520 


93 526 


93 531 


93 536 


93 541 


93 546 


862 


93 551 


93 556 


93 561 


93 566 


93 571 


93 576 


93 581 


93 586 


93 591 


93 596 


863 


93 601 


93 606 


93 611 


93 616 


93 621 


93 626 


93 631 


93 636 


93 641 


93 646 


864 


93 651 


93 656 


93 661 


93 666 


93 671 


93 676 


93 682 


93 687 


93 692 


93 697 


865 


93 702 


93 707 


93 712 


93 717 


93 722 


93 727 


93 732 


93 737 


93 742 


93 747 


866 


- 93 752 


93 757 


93 762 


93 767 


93 772 


93 777 


93 782 


93 787 


93 792 


93 797 


867 


93 802 


93 807 


93 812 


93 817 


93 822 


93 827 


93 832 


93 837 


93 842 


93 847 


868 


93 852 


93 857 


93 862 


93S67 


93 872 


93 877 


93 882 


93 887 


93 892 


93 897 


869 


93 902 


93 907 


93 912 


93 917 


93 922 


93 927 


93 932 


93 937 


93 942 


93 947 


870 


93 952 


93 957 


93 962 


93 967 


93 972 


93 977 


93 982 


93 987 


93 992 


93 997 


871 


94 002 


94 007 


94 012 


94 017 


94 022 


94 027 


94 032 


94 037 


94 042 


94 047 


872 


94 052 


94 057 


94 062 


94 067 


94 072 


94 077 


94 082 


94 086 


94 091 


94 096 


873 


94101 


94 106 


94111 


94116 


94121 


94 126 


94 131 


94 136 


94 141 


94146 


874 


94151 


94156 


94161 


94166 


94 171 


94176 


94 181 


94 186 


94191 


94196 


875 


94 201 


94 206 


94 211 


94 216 


94 221 


94 226 


94 231 


94 236 


94 240 


94 245 


876 


94 250 


94 255 


94 260 


94 265 


94 270 


94 275 


94 280 


94 285 


94 290 


94 295 


877 


94 300 


94 305 


94 310 


94 315 


94 320 


94 325 


94 330 


94 335 


94 340 


94 345 


878 


94 349 


94 354 


94 359 


94 364 


94 369 


94 374 


94 379 


94 384 


94 389 


94 394 


879 


94 399 


94 404 


94 409 


94 414 


94 419 


94 424 


94 429 


94 433 


94 438 


94 443 


880 


94 448 


94 453 


94 458 


94 463 


94 468 


94 473 


94 478 


94 483 


94 488 


94 493 


881 


94 498 


94 503 


94 507 


94 512 


94 517 


94 522 


94 527 


94 532 


94 537 


94 542 


882 


94 547 


94 552 


94 557 


94 562 


94 567 


94 571 


94 576 


94 581 


94 586 


94 591 


883 


94 596 


94 601 


94 606 


94 611 


94 616 


94 621 


94 626 


94 630 


94 635 


94 640 


884 


94 645 


94 650 


94 655 


94 660 


94 665 


94 670 


94 675 


94 680 


94 685 


94 689 


885 


94 694 


94 699 


94 704 


94 709 


94 714 


94 719 


94 724 


94 729 


94 734 


94 73S 


886 


94 743 


94 748 


94 753 


94 758 


94 763 


94 76S 


94 773 


94 778 


94 783 


94 787 


887 


94 792 


94 797 


94 802 


94 807 


94 812 


94 817 


94 822 


94 827 


94 832 


94 836 


888 


94 841 


94 846 


94 851 


94 856 


94 861 


94 866 


94 871 


94 876 


94 880 


94 885 


889 


94 890 


94 895 


94 900 


94 905 


94 910 


94 915 


94 919 


94 924 


94 929 


94 934 


890 


94 939 


94 944 


94 949 


94 954 


94 959 


94 963 


94 968 


94 973 


94 978 


94 983 


891 


94 988 


94 993 


94 998 


95 002 


95 007 


95 012 


95 017 


95 022 


95 027 


95 032 


•892 


95 036 


95 041 


95 046 


95 051 


95 056 


95 061 


95 066 


95 071 


95 075 


95 080 


893 


95 085 


95 090 


95 095 


95 100 


95 105 


95 109 


95 114 


95 119 


95 124 


95 129 


894 


95 134 


95 139 


95143 


95 148 


95 153 


95 158 


95 163 


95 16S 


95 173 


95177 


895 


95 182 


95 187 


95 192 


95 197 


95 202 


95 207 


95 211 


95 216 


95 221 


95 226 


896 


95 231 


95 236 


95 240 


95 245 


95 250 


95 255 


95 260 


95 265 


95 270 


95 274 


897 


95 279 


95 284 


95 289 


95 294 


95 299 


95 303 


95 308 


95 313 


95 31S 


95 323 


898 


95 328 


95 332 


95 337 


95 342 


95 347 


95 352 


95 357 


95 361 


95 366 


95 371 


899 


95 376 


95 381 


95 386 


95 390 


95 395 


95 400 


95 405 


95 410 


95 415 


95 419 


900 


95 424 


95 429 


95 434 
2 


95 439 


95 444 


95 448 


95 453 


95 458 


95 463 


95 468 


N 


O 


1 


3 


4 


5 


6 


7 


8 


9 



850-900 



18 



900-950 



N 





1 
95 429 


2 


3 4 


5 


6 


7 


8 


9 


900 


95 424 


95 434 


95 439 95 444 


95 448 


95 453 


95 458 


95 463 


95 468 


901 


95 472 


95 477 


95 482 


95 487 95 492 


95 497 


95 501 


95 506 


95 511 


95 516 


902 


95 521 


95 525 


95 530 


95 535 95 540 


95 545 


95 550 


95 554 


95 559 


95 564 


903 


95 569 


95 574 


95 578 


95 583 95 588 


95 593 


95 598 


95 602 


95 607 


95 612 


904 


95 617 


95 622 


95 626 


95 631 95 636 


95 641 


95 646 


95 650 


95 655 


95 660 


905 


95 665 


95 670 


95 674 


95 679 95 684 


95 689 


95 694 


95 698 


95 703 


95 708 


906 


95 713 


95 718 


95 722 


95 727 95 732 


95 737 


95 742 


95 746 


95 751 


95 756 


907 


95 761 


95 766 


95 770 


95 775 95 780 


95 785 


95 789 


95 794 


95 799 


95 804 


908 


95 809 


95 813 


95 818 


95 823 95 828 


95 832 


95 837 


95 842 


95 847 


95 852 


909 


95 856 


95 861 


95 866 


95 871 95 875 


95 880 


95 885 


95 890 


95 895 


95 899 


910 


95 904 


95 909 


95 914 


95 918 95 923 


95 928 


95 933 


95 938 


95 942 


95 947 


911 


95 952 


95 957 


95 961 


95 966 95 971 


95 976 


95 980 


95 985 


95 990 


95 995 


912 


95 999 


96 004 


96 009 


96 014 96 019 


96 023 


96 028 


96 033 


96 038 


96 042 


913 


96 047 


96 052 


96 057 


96 061 96 066 


96 071 


96 076 


96 080 


96 085 


96 090 


914 


96 095 


96 099 


96104 


96109 96114 


96118 


96 123 


96128 


96133 


96137 


915 


96142 


96147 


96152 


96156 96 161 


96166 


96 171 


96175 


96180 


96185 


916 


96190 


96194 


96199 


96 204 96 209 


96 213 


96 218 


96 223 


96 227 


96 232 


917 


96 237 


96 242 


96 246 


96 251 96 256 


96 261 


96 265 


96 270 


96 275 


96 280 


918 


96 284 


96 289 


96 294 


96 298 96 303 


96 308 


96 313 


96 317 


96 322 


96 327 


919 


96 332 


96 336 


96 341 


96 346 96 350 


96 355 


96 360 


96 365 


96 369 


96 374 


920 


96 379 


96 384 


96 388 


96 393 96 398 


96 402 


96 407 


96 412 


96 417 


96 421 


921 


96 426 


96 431 


96 435 


96 440 96 445 


96 450 


96 454 


96 459 


96 464 


96 468 


922 


96 473 


96 478 


96 483 


96 487 96 492 


96 497 


96 501 


96 506 


96 511 


96 515 


923 


96 520 


96 525 


96 530 


96 534 96 539 


96 544 


96 548 


96 553 


96 558 


96 562 


924 


96 567 


96 572 


96 577 


96 581 96 586 


96 591 


*96 595 


96 600 


96 605 


96 609 


925 


96 614 


96 619 


96 624 


96 628 96 633 


96 638 


'96 642 


•96 647 


96 652 


96 656 


926 


96 661 


96 666 


96 670 


96 675 96 680 


96 685 


96 689 


96 694 


96 699 


96 703 


927 


96 708 


96 713 


96 717 


96 722 96 727 


96 731 


96 736 


96 741 


96 745 


96 750 


928 


96 755 


96 759 


96 764 


96 769 96 774 


96 778 


96 783 


96 788 


96 792 


96 797 


929 


96 802 


96 806 


96 811 


96 816 96 820 


96 825 


96 830 


96 834 


96 839 


96 844 


930 


96 848 


96 853 


96 858 


96 862 96 867 


96 872 


96 876 


96 881 


96 886 


96 890 


931 


96 895 


96 900 


96 904 


96 909 96 914 


96 918 


96 923 


96 928 


96 932 


96 937 


932 


96 942 


96 946 


96 951 


96 956 96 960 


96 965 


96 970 


96 974 


96 979 


96 984 


933 


96 988 


96 993 


96 997 


97 002 97 007 . 


97 011 


97 016 


97 021 


97 025 


97 030 


934 


97 035 


97 039 


97 044 


97 049 97 053 


97 058 


97 063 


97 067 


97 072 


97 077 


935 


97 081 


97 086 


97 090 


97 095 97100 


97104 


97109 


97114 


97118 


97123 


936 


97128 


97132 


97137 


97142 97 146 


97151 


97155 


97160 


97 165 


97169 


937 


97174 


97179 


97183 


97 188 97 192 


97197 


97 202 


97 206 


97 211 


97 216 


938 


97 220 


97 225 


97 230 


97 234 97 239 


97 243 


97 248 


97 253 


97 257 


97 262 


939 


97 267 


97 271 


97 276 


97 280. 97 2S5 . 


97 290 


97 294 


97 299 


97 304 


97 308 


940 


97 313 


97 317 


97 322 


97 327 97 331 


97 336 


97 340 


97 345 


97 350 


97 354 


941 


97 359 


97 364 


97 368 


97 373 97 377 


97 382 


97 387 


97 391 


97 396 


97 400 


942 


97 405 


97 410 


97 414 


97 419 97 424 


97 428 


97 433 


97 437 


97 442 


97 447 


943 


97 451 


97 456 


97 460 


97 465 97 470 


97 474 


97 479 


97 483 


97 488 


97 493 


944 


97 497 


97 502 


97 506 


97 511 97 516 


97 520 


97 525 


97 529 


97 534 


97 539 


945 


97 543 


97 548 


97 552 


97 557 97 562 


97 566 


97 571 


97 575 


97 580 


97 585 


946 


97 589 


97 594 


97 598 


97 603 97 607 


97 612 


97 617 


97 621 


97 626 


97 630 


947 


97 635 


97 640 


97 644 


97 649 97 653 


97 658 


97 663 


97 667 


97 672 


97 676 


948 


97 681 


97 685 


97 690 


97 695 97 699 


97 704 


97 70S 


97 713 


97 717 


97 722 


949 


97 727 


97 731 


97 736 


97 740 97 745 


97 749 


97 754 


97 759 


97 763 


97 768 


1 950 


97 772 


97 777 


97 782 


97 786 97 791 


97 795 


97 800 


97 804 


97 809 


97 813 


1 N 


O 


1 


2 


3 4 


5 


6 


7 


8 


9 



900-950 











950-1000 








19 


N 





1 


2 


3 


4 


5 


6 


7 


8 

97 809 


9 


950 


97 772 


97 777 


97 782 


97 786 


97 791 


97 795 


97 800 


97 804 


97 813 


951 


97 818 


97 823 


97 827 


97 832 


97 836 


97 841 


97 845 


97 850 


97 855 


97S59 


952 


97 864 


97 86S 


97 873 


97S77 


97 882 


97 886 


97 891 


97 896 


97 900 


97 905 


953 


97 909 


97 914 


97 918 


97 923 


97 928 


97 932 


97 937 


97 941 


97 946 


97 950 


954 


97 955 


97 959 


97 964 


97 96S 


97 973 


97 978 


97 982 


97 987 


97 991 


97 996 


955 


98 000 


98 005 


98 009 


9S014 


98 019 


98 023 


98 028 


98 032 


98 037 


9S041 


956 


98 046 


98 050 


9S055 


98 059 


98 064 


98 068 


98 073 


98 078 


98 082 


98 087 


957 


98 091 


98 096 


98100 


98 105 


9S109 


98 114 


98 118 


98 123 


98127 


9S132 


958 


98137 


98141 


98146 


98 150 


98155 


98159 


98164 


98168 


98173 


9S177 


959 


98182 


98186 


98 191 


98195 


98 200 


98 204 


98 209 


98 214 


98 218 


98 223 


960 


98 227 


98 232 


98 236 


98 241 


98 245 


98 250 


98 254 


98 259 


98 263 


98 268 


961 


98 272 


98 277 


98 281 


98 286 


98 290 


98 295 


98 299 


98 304 


98 308 


98 313 


962 


98 318 


98 322 


98 327 


9S331 


98 336 


98 340 


98 345 


98 349 


98 354 


98 358 


963 


98 363 


98 367 


9S372 


98 376 


98 381 


98 385 


98 390 


98 394 


98 399 


98 403 


964 


98 408 


98 412 


98 417 


98 421 


98 426 


98 430 


98 435 


98 439 


98 444 


98 448 


965 


98 453 


98 457 


9S462 


98 466 


98 471 


98 475 


98 480 


98 484 


98 489 


98 493 


966 


98 498 


98 502 


9S507 


9S511 


98 516 


98 520 


98 525 


98 529 


98 534 


98 538 


967 


98 543 


98 547 


9S552 


98 556 


98 561 


98 565 


9S570 


98 574 


98 579 


98 583 


968 


98 588 


98 592 


98 597 


98 601 


98 605 


98 610 


98 614 


98 619 


98 623 


98 628 


969 


98 632 


98 637 


98 641 


9S646 


98 650 


98 655 


98 659 


98 664 


98 668 


98 673 


970 


98 677 


98 682 


9S686 


98 691 


98 695 


98 700 


98 704 


98 709 


98 713 


98 717 


971 


98 722 


98 726 


98 731 


98 735 


98 740 


98 744 


98 749 


98 753 


98 758 


98 762 


972 


98 767 


98 771 


98 776 


98 780 


98 784 


98 789 


98 793 


98 798 


98 802 


98 807 


,973 


98 811 


98 816 


98 820 


98 825 


98 829 


98 834 


98 838 


9$843 


98 847 


98 851 


974 


98 856 


9S860 


9SS65 


98 869 


98 874 


98 878 


98 883 


98 887 


98 892 


98 896 


975 


98 900 


98 905 


98 909 


98 914 


98 918 


98 923 


9S927 


98 932 


98 936 


98 941 


976 


9S945 


98 949 


98 954 


98 958 


98 963 


98 967 


98 972 


98 976 


98 981 


98 985 


977 


98 989 


98 994 


98 998 


99 003 


99 007 


99 012 


99 016 


99 021 


99 025 


99 029 


978 


99 034 


99 038 


99 043 


99 047 


99 052 


99 056 


99 061 


99 065 


99 069 


99 074 


979 


99 07S 


99 083 


99 0S7 


99 092 


99 096 


99 100 


99105 


99109 


99114 


99118 


980 " 


99123 


99127 


99131 


99136 


99140 


99145 


99149 


99154 


99158 


99162 


981 


99167 


99171 


99176 


99 180 


99 185 


99189 


99193 


99198 


99 202 


99 207 


982 


99 211 


99 216 


99 220 


99 224 


99 229 


99 233 


99 238 


99 242 


99 247 


99 251 


983 


99 255 


99 260 


99 264 


99 269 


99 273 


99 277 


99 282 


99 286 


99 291 


99 295 


984 


99 300 


99 304 


99 308 


99 313 


99 317 


99 322 


99 326 


99 330 


99 335 


99 339 


985 


99 344 


99 348 


99 352 


99 357 


99 361 


99 366 


99 370 


99 374 


99 379 


99 383 


986 


99 388 


99 392 


99 396 


99 401 


99 405 


99 410 


99 414 


99 419 


99 423 


99 427 


987 


99 432 


99 436 


99 441 


99 445 


99 449 


99 454 


99 458 


99 463 


99 467 


99 471 . 


988 


99 476 


99 480 


99 484 


99 489 


99 493 


99 498 


99 502 


99 506 


99 511 


99 515 


989 


99 520 


99 524 


99 528 


99 533 


99 537 


99 542 


99 546 


99 550 


99 555 


99 559 


990 


99 564 


99 568 


99 572 


99 577 


99 581 


99 585 


99 590 


99 594 


99 599 


99 603 


991 


99 607 


99 612 


99 616 


99 621 


99 625 


99 629 


99 634 


99 638 


99 642 


99 647 


992 


99 651 


99 656 


99 660 


99 664 


99 669 


99 673 


99 677 


99 682 


99 686 


99 691 


993 


99 695 


99 699 


99 704 


99 708 


99 712 


99 717 


99 721 


99 726 


99 730 


99 734 


994 


99 739 


99 743 


99 747 


99 752 


99 756 


99 760 


99 765 


99 769 


99 774 


99 778 


995 


99 782 


99 787 


99 791 


99 795 


99 800 


99 804 


99 808 


99 813 


99 817 


99 822 


996 


99 826 


99 830 


99 835 


99 839 


99 843 


99 848 


99 852 


99 856 


99 861 


99 865 


997 


99 870 


99 874 


99 878 


99 883 


99 887 


99 891 


99 896 


99 900 


99 904 


99 909 


998 


99 913 


99 917 


99 922 


99 926 


99 930 


99 935 


99 939 


99 944 


99 948 


99 952 


999 


99 957 


99 961 


99 965 


99 970 


99 974 


99 978 


99 983 


99 987 


99 991 


99 996 


1000 


00 000 


00 004 


00 009 


00 013 


00 017 


00 022 


00 026 


00 030 


00 035 


00 039 


N 


O 


1 


2 


3 


4 


5 


6 


7 


8 


9 



950-1000 



20 TABLE II. -LOGARITHMS OF CONSTANTS. 



Circumference of the Circle in degrees = 360 

Circumference of the Circle in minutes = 21 600 

Circumference of the Circle in seconds =1 296 000 

If the radius r = 1, half the Circumference of the Circle is 
7T = 3. 14 159 265 358 979 323 846 264 338 328 



log 
2. 55 630 250 
4. 33 445 375 
6. 11 260 500 

0. 49 714 987 



Also : 
2tt= 6.28 318 531 

4tt = 12.56 637 061 

£ = 1.57 079 633 

2 

- = 1.04 719 755 



— = 4.18 879 020 
3 

£= 0.78 539 816 
4 

- = 0.52 359 878 
6 

-= 0.31830 989 



2*" 
3 



47T 



■ = 0.15 915 494 

= 0.95 492 966 

= 1.27 323 954 

= 0.23 873 241 



log- 

0. 79 817 987 

1. 09 920 986 
0. 19 611 988 

0. 02 002 862 

0. 62 208 861 

9. 89 508 988 - 10 

9. 71 899 862 - 10 

9. 50 285 013 - 10 

9. 20 182 013 - 10 

9. 97 997 138 - 10 

0. 10 491 012 

9. 37 791 139 - 10 



1 

4- 

3/„ — 
y/ir — 

1 _ 

3)_3_ 



= 9. 86 960 440 
= 0. 10 132 118 
= 1. 77 245 385 
= 0.56 418 958 

= 0. 97 720 502 



1.12 837 917 
1. 46 459 1S9 
0.68 278 406 

2. 14 502 940 
0. 62 035 049 

0. SO 599 598 



log 
0. 99 429 975 

9. 00 570 025 - 10 
0.24 857494 

9. 75 142 506 - 10 

9. 98 998 569 - 10 

0. 05 245 506 
0. 16 571 662 
9. 83 428 338 - 10 

0. 33 143 325 

9. 79 263 713 - 10 

9. 90 633 287 - 10 



Arc a, whose length is equal to the radius r, is : 

180 



in degrees a 

in minutes a' 

in seconds a" 



10 800 



648 000 



= 57.29 577 951°. 
= 3 437. 74 677' . . 
= 206 264. 806" . . 



Arc 2 a, whose length is equal to twice the radius, 2 r, is 

360 



in degrees 2 a° . . . . = . . . 

7T 

21600 



in minutes 2 a' : 



in seconds 2 a" .... = 



1 296 000 



If the radius r = 1, the length of the arc is-; 

180 " 



for 1 degree .... 
for 1 minute .... 

for 1 second 

for J degree 

for I- minute. . . . 



for \ second 



or 
_1 
a'"' 

J_ 

a"'" 
1 

2tt°' 
1 

2 a'" 
1 

2 a"' 



10 800 

IT 

648 000 ' 

IT 

360"" 



21600 



= 114. 59 155 903° 
= 6 875.49 354'.. 
= 412 529. 612" . . 

= 0. 01 745 329. . . 

= 0. 00 029 089. . . 

= 0.00 000 485... 
. = 0. 00 872 665. . . 
. = 0. 00 014 544. . . 

= 0.00 000 242... 



1 296 000 
Sin 1" in the unit circle = 0. 00 000 485. , 



log 
1. 75 812 263 

3. 53 627 388 

5.31442 513 

2. 05 915 263 

3. 83 730 388 
5. 61 545 513 

8. 24 187 737 - 10 
6.46372 612-10 

4.68 557487-10 
7. 94 0S4 737 - 10 
6. 16 269 612 - 10 

4. 38 454 487 - 10 
4. 68 557 487 - 10 



21 









TABLE III. 












THE LOGARITHMS 
















OF THE 












TRIGONOMETRIC 


FUNCTIONS : 








From 0° to 0° 3', or 89° 57' to 90°, for every second ; 










From 0° to 2°, or 88° 


to 90°, for 


every ten seconds ; 








Prom 1° t( 
Note. T 

log sin 


) 89°, for every minute 


is to be appended. 

log tan = log sin 
log cos = 10, 00 000 






o all the logarithms — ] 






0° 


tt 


0' 


1' 


2' 


tt 


tt 


0' 


1' 


2' 


tt 
30 





. 


6. 46 373 


6. 76 476 


60 


30 


6. 16 270 


6. 63 982 


6. 86 167 


1 


4. 68 557 


6. 47 090 


6. 76 836 


59 


31 


6. 17 694 


6. 64 462 


6. 86 455 


29 


2 


4. 9S 660 


6. 47 797 


6. 77 193 


5S 


32 


6. 19 072 


6. 64 936 


6. 86 742 


28 


3 


5. 16 270 


6. 48 492 


6. 77 548 


57 


33 


6. 20 409 


6. 65 406 


6. 87 027 


27 


■4 


5. 2S 763 


6.49175 


6. 77 900 


56 


34 


6. 21 705 


6. 65 870 


6.87 310 


26 


5 


5. 38 454 


6. 49 849 


6. 78 24S 


55 


35 


6. 22 964 


6.66 330 


6. 87 591 


25 


6 


5. 46 373 


6.50 512 


6. 78 595 


54 


36 


6. 24 188 


6. 66 785 


6. 87 870 


24 


7 


5. 53 067 


6. 51 165 


6. 78 938 


53 


37 


6. 25 378 


6. 67 235 


6. 88 147 


23 


8 


5. 58 866 


6. 51 808 


6. 79 278 


52 


38 


6. 26 536 


6. 67 680 


6. 88 423 


22 


9 


5. 63 982 


6. 52 442 


6. 79 616 


51 


39 


6. 27 664 


6. 68 121 


6. 88 697 


21 


10 


5. 6S557 


6. 53 067 


6. 79 952 


50 


40 


6. 28 763 


6. 68 557 


6. SS 969 


20 


11 


5.72 697 


6. 53 683 


6. 80 285 


49 


41 


6. 29 836 


6. 68 990 


6. 89 240 


19 


12 


5. 76 476 


6. 54 291 


6. 80 615 


4S 


42 


6. 30 882 


6. 69 418 


6. 89 509 


18 


13 


5.79 952 


6. 54 890 


6. 80 943 


47 


43 


6. 31 904 


6. 69 841 


6. 89 776 


17 


14 


5. S3 170 


6. 55 481 


6. 81 26S 


46 


44 


6. 32 903 


6. 70 261 


6. 90 042 


16 


15 


5. 86 167 


6. 56 064 


6. 81 591 


45 


45 


6. 33 879 


6. 70 676 


6. 90 306 


15 


16 


5.88 969 


6. 56 639 


6.81911 


44 


46 


6. 34 833 


6. 71 088 


6. 90 568 


14 


17 


5. 91 602 


6. 57 207 


6. 82 230 


43 


47 


6. 35 767 


6. 71 496 


6. 90 829 


13 


18 


5. 94 085 


6. 57 767 


6. 82 545 


42 


48 


6. 36 682 


6. 71 900 


6. 91 088 


12 


19 


5.96 433 


6. 58 320 


6. 82 859 


41 


49 


6.37 577 


6. 72 300 


6. 91 346 


11 


20 


5. 98 660 


6. 58 866 


6. 83 170 


40 


50 


6. 38 454 


6. 72 697 


6. 91 602 


10 


21 


6. 00 779 


6. 59 406 


6. 83 479 


39 


51 


6.39 315 


6. 73 090 


6. 91 857 


9 


22 . 


6. 02 800 


6. 59 939 


6. S3 786 


38 


52 


6. 40 158 


6. 73 479 


6. 92 110 


8 


23 


6. 04 730 


6. 60 465 


6. 84 091 


37 


53 


6. 40 985 


6. 73 865 


6. 92 362 


7 


24 


6. 06 579 


6. 60 985 


6. 84 394 


36 


54 


6. 41 797 


6. 74 248 


6. 92 612 


6 


25 


6. OS 351 


6.61499 


6. 84 694 


35 


55 


6. 42 594 


6. 74 627 


6. 92 S61 


5 


26 


6.10 055 


6. 62 007 


6. 84 993 


34 


56 


6. 43 376 


6. 75 003 


6. 93 109 


4 


27 


6. 11 694 


6. 62 509 


6. 85 289 


33 


57 


6. 44 145 


6. 75 376 


6. 93 355 


3 


2S 


6. 13 273 


6. 63 006 


6. 85 5S4 


32 


58 


6. 44 900 


6. 75 746 


6. 93 599 


2 


29 


6. 14 797 


6. 63 496 


6. S5 876 


31 


59 


6. 45 643 


6. 76 112 


6. 93 843 


1 


30 

ft 


6. 16 270 


6. 63 982 


6. S6 167 


30 


60 


6. 46 373 


6.76 476 


6. 94 085 





59' 


58' 


57' 


tt 


tt 


59' 


58' 


57' 


ft 



log cot = log cos 
log sin = 10. 00 000 



89 c 



log cos 



22 








0° 








t tt 


log sin 


log tan 


log COS 


ft I 


t tt 


log sin log tan 


log COS 


tt t 








10 00000 


60 


10 


7. 46 373 7. 46 373 


10.00000 


50 


10 


5.68 557 


5. 68 557 


30.00000 


50 


10 


7. 47 090 7. 47 091 


10.00000 


50 


20 


5.98 660 


5.98 660 


10 00000 


40 


20 


7.47 797 7.47 797 


10.00000 


40 


30 


6. 16 270 


6. 16 270 


10.00000 


30 


30 


7. 48 491 7. 48 492 


10 00000 


30 


' 40 


6. 28 763 


6. 28 763 


10.00000 


20 


40 


7. 49 175 7. 49 176 


10.00000 


20 


50 


6. 38 454 


6. 38 454 


10.00000 


10 


50 


7. 49 849 7. 49 849 


10.00000 


10 


1 


6.46 373 


6. 46 373 


10 00000 


59 


110 


7.50 512 7.50 512 


10.00000 


49 


10 


6. 53 067 


6. 53 067 


10.00000 


50 


10 


7. 51 165 7. 51 165 


10.00000 


50 


20 


6. 58 866 


6. 58 866 


1000000 


40 


20 


7.51808 7.51809 


10.00000 


40 


30 


6. 63 9S2 


6. 63 982 


1000000 


30 


30 


7. 52 442 7. 52 443 


10.00000 


30 


40 


6. 68 557 


6. 68 557 


10.00000 


20 


40 


7. 53 067 7. 53 067 


10 00000 


20 


SO 


6. 72 697 


6. 72 697 


1000000 


10 


50 


7. 53 683 7. 53 683 


10.00000 


10 


2 


6.76 476 


6.76 476 


10 00000 


58 


12 


7. 54 291 7. 54 291 


10 00000 


48 


10 


6. 79 952 


6. 79 952 


10.00000 


50 


10 


7. 54 890 7. 54 890 


10 00000 


50 


20 


6 83 170 


6. 83 170 


10.00000 


40 


20 


7. 55 481 7. 55 481 


10 00000 


40 


30 


6. 86 167 


6. 86 167 


10 00000 


30 


30 


7.56 064 7.56 064 


10.00000 


30 


40 


6. 8S 969 


6. 88 969 


10 00000 


20 


40 


7. 56 639 7. 56 639 


10.00000 


20 


50 


6. 91 602 


6. 91 602 


10.00000 


10 


50 


7. 57 206 7. 57 207 


10.00000 


10 


3 


6. 94 085 


6. 94 0S5 


10 00000 


057 


13 


7. 57 767 7. 57 767 


10.00000 


047 


10 


6 96 433 


6. 96 433 


10 00000 


50 


10 


7.58 320 7.58 320 


10.00000 


50 


20 


6. 98 660 


6. 98 661 


10 00000 


40 


20 


7.58 866 7.58 867 


10 00000 


40 


30 


7. 00 779 


7. 00 779 


10 00000 


30 


30 


7. 59 406 7. 59 406 


10.00000 


30 


40 


7. 02 800 


7. 02 800 


10 00000 


20 


40 


7. 59 939 7. 59 939 


10.00000 


20 


50 


7. 04 730 


7. 04 730 


10.00000 


10 


50 


7. 60 465 7. 60 466 


10.00000 


10 


4 


7. 06 579 


7.06 579 


10.00000 


56 


14 


7. 60 985 7. 60 986 


10.00000 


46 


10 


7. OS 351 


7. 08 352 


10.00000 


50 


10 


7. 61 499 7. 61 500 


10.00000 


50 


20 


7.10 055 


7. 10 055 


1000000 


40 


20 


7. 62 007 7. 62 008 


10.00000 


40 


30 


7.11694 


7. 11 694 


10.00000 


30 


30 


7. 62 509 7. 62 510 


10.00000 


30 


40 


7. 13 273 


7. 13 273 


1000000 


20 


40 


7. 63 006 7. 63 006 


10.00000 


20 


50 


7. 14 797 


7. 14 797 


10.00000 


10 


50 


7. 63 496 7. 63 497 


10.00000 


10 


5 


7. 16 270 


7. 16 270 


10 00000 


55 


15 


7.63 982 .7.63 982 


10.00000 


45 


10 


7. 17 694 


7. 17 694 


10.00000 


50 


10 


7. 64 461 7. 64 462 


10.00000 


50 


20 


7. 19 072 


7. 19 073 


10.00000 


40 


20 


7.64 936. 7.64 937 


10.00000 


40 


30 


7. 20 409 


7. 20 409 


10.00000 


30 


30 


7. 65 406 7. 65 406 


10.00000 


30 


40 


7. 21 705 


7. 21 705 


10 00000 


20 


40 


7.65 870 7.65 871 


10.00000 


20 


50 


7. 22 964 


7. 22 964 


10.00000 


10 


50 


7. 66 330 7. 66 330 


10.00000 


10 


6 


7. 24 188 


7. 24 188 


10.00000 


54 


16 


7.66 784 7.66 785 


10.00000 


44 


10 


7. 25 378 


7. 25 378 


10.00000 


50 


10 


7. 67 235 7. 67 235 


10.00000 


50 


20 


7. 26 536 


7.26536 


10.00000 


40 


20 


7. 67 6S0 7. 67 680 


10.00000 


40 


30 


7. 27 664 


7. 27 664 


10.00000 


30 


30 


7.68121 7. 68 121 


10.00000 


30 


40 


7. 28 763 


7. 28 764 


10.00000 


20 


• 40 


7.68 557 7.68 558 


9.99999 


20 


50 


7. 29 836 


7. 29 836 


10.00000 


10 


50 


7. 68 989 7. 68 990 


9.99999 


10 


7 


7. 30 882 


7. 30 882 


10.00000 


53 


170 


7. 69 417 7. 69 418 


9. 99 999 


43 


10 


7. 31 904 


7. 31 904 


10.00000 


50 


10 


7. 69 841 7. 69 842 


9. 99 999 


50 


20 


7. 32 903 


7. 32 903 


10.00000 


40 


20 


7. 70 261 7. 70 261 


9. 99 999 


40 


30 


7. 33 879 


7. 33 879 


10.00000 


30 


30 


7. 70 676 7. 70 677 


9. 99 999 


30 


40 


7. 34 833 


7. 34 833 


10.00000 


20 


40 


7.71088 7.71088 


9. 99 999 


20 


50 


7. 35 767 


7. 35 767 


10.00000 


10 


50 


7. 71 496 7. 71 496 


9. 99 999 


10 


8 


7. 36 682 


7. 36 682 


10.00000 


52 


18 


7. 71 900 7. 71 900 


9. 99 999 


42 


10 


7.37 577 


7.37 577 


10.00000 


50 


10 


7. 72 300 7. 72 301 


9. 99 999 


50 


20 


7. 38 454 


7. 38 455 


10.00000 


40 


20 


7. 72 697 7. 72 697 


9. 99 999 


40 


30 


7.39 314 


7.39 315 


10.00000 


30 


30 


7. 73 090 7. 73 090 


9. 99 999 


30 


40 


7. 40 158 


7. 40 158 


10.00000 


20 


40 


7. 73 479 7. 73 480 


9. 99 999 


20 


50 


7. 40 985 


7. 40 985 


10.00000 


10 


50 


7. 73 865 7. 73 866 


9. 99 999 


10 


9 


7. 41 797 


7. 41 797 


10.00000 


051 


190 


7. 74 248 7. 74 248 


9. 99 999 


041 


10 


7. 42 594 


7. 42 594 


10.00000 


50 


10 


7. 74 627 7. 74 628 


9. 99 999 


50 


20 


7. 43 376 


7. 43 376 


10 00000 


40 


20 


7. 75 003 7. 75 004 


9. 99 999 


40 


30 


7. 44 145 


7. 44 145 


10.00000 


30 


30 


7.75 376 7.75 377 


9. 99 999 


30 


40 


7. 44 900 


7. 44 900 


10.00000 


20 


40 


7. 75 745 7. 75 746 


9. 99 999 


20 


50 


7. 45 643 


7. 45 643 


10.00000 


10 


50 


7. 76 112 7. 76 113 


9. 99 999 


10 


100 


7. 46 373 


7.46373 


10.00000 


50 


20 


7.76 475 7.76476 


9. 99 999 


4O 


t tt 


log cos 


log cot 


log sin . 


tt t 


t tt 


log cos log cot 


log sin 


tt t 



89 c 











0° 








23 


t " 


log sin 


log tan 


log cos 


ft t 


t tr 


log sin 


log tan 


log COS 


rt t 


20 


7. 76 475 


7. 76 476 


9. 99 999 


40 


30 


7. 94 084 


7. 94 086 


9. 99 998 


30 


10 


7. 76 836 


7. 76 837 


9. 99 999 


50 


10 


7. 94 325 


7. 94 326 


9. 99 998 


50 


20 


7. 77 193 


7. 77 194 


9. 99 999 


40 


20 


7. 94 564 


7. 94 566 


9. 99 998 


40 


30 


7. 77 548 


7. 77 549 


9. 99 999 


30 


30 


7. 94 802 


7. 94 804 


9. 99 99S 


30 


40 


7. 77 899 


7. 77 900 


9. 99 999 


20 


40 


7. 95 039 


7. 95 040 


9. 99 998 


20 


50 


.7. 78 248 


7. 78 249 


9. 99 999 


10 


50 


7. 95 274 


7. 95 276 


9. 99 998 


10 


210 


7. 78 594 


7. 78 595 


9. 99 999 


39 


31 


7. 95 508 


7.95 510 


9. 99 998 


29 


10 


7. 78 938 


7. 78 938 


9. 99 999 


50 


10 


7. 95 741 


7. 95 743 


9. 99 998 


50 


20 


7. 79 278 


7. 79 279 


9. 99 999 


40 


20 


7. 95 973 


7. 95 974 


9. 99 998 


40 


30 


7. 79 616 


7.79 617 


9. 99 999 


30 


30 


7. 96 203 


7. 96 205 


9. 99 998 


30 


40 


7. 79 952 


7. 79 952 


9. 99 999 


20 


40 


7. 96 432 


7. 96 434 


9. 99 998 


20 


50 


7. 80 284 


7. SO 285 


9. 99 999 


10 


50 


7. 96 660 


7. 96 662 


9. 99 998 


10 


220 


7. 80 615 


7. SO 615 


9. 99 999 


38 


32 


7. 96 887 


7. 96 889 


9. 99 998 


28 


10 


7. 80 942 


7. SO 943 


9. 99 999 


50 


10 


7. 97 113 


7. 97 114 


9. 99 998 


50 


20 


7. 81 26S 


7. 81 269 


9. 99 999 


40 


20 


7. 97 337 


7. 97 339 


9. 99 998 


40 


30 


7. SI 591 


7. 81 591 


9. 99 999 


30 


30 


7. 97 560 


7. 97 562 


9. 99 998 


30 


40 


7. SI 911 


7.81912 


9. 99 999 


20 


40 


7. 97 7S2 


7. 97 784 


9. 99 998 


20 


50 


7. 82 229 


7. 82 230 


9. 99 999 


10 


50 


7. 98 003 


7. 98 005 


9. 99 998 


10 


230 


7. 82 545 


7. 82 546 


9. 99 999 


37 


33 


7. 98 223 


7. 98 225 


9. 99 998 


27 


10 


7.S2S59 


7. 82 860 


9. 99 999 


50 


10 


7. 98 442 


7. 98 444 


9. 99 998 


50 


20 


7.83 170 


7. 83 171 


9. 99 999 


40 


20 


7. 98 660 


7. 98 662 


9. 99 998 


40 


30 


7. 83 479 


7. S3 480 


9. 99 999 


30 


30 


7. 9S 876 


7. 98 878 


9. 99 998 


30 


40 


7. 83 786 


7. S3 787 


9. 99 999 


20 


40 


7. 99 092 


7. 99 094 


9. 99 998 


20 


50 


7. 84 091 


7. S4 092 


9. 99 999 


10 


50 


7.99 306 


7. 99 308 


9. 99 998 


10 


240 


7. 84 393 


7. 84 394 


9. 99 999 


36 


34 


7. 99 520 


7. 99 522 


9. 99 998 


26 


10 


7. 84 694 


7. 84 695 


9. 99 999 


50 


10 


7. 99 732 


7. 99 734 


9. 99 998 


50 


20 


7. 84 992 


7. 84 994 


9. 99 999 


40 


20 


7. 99 943 


7. 99 946 


9. 99 998 


40 


30 


7. 85 289 


7. S5 290 


9. 99 999 


30 


30 


8. 00 154 


8.00156 


9. 99 998 


30 


40 


7. 85 583 


7. 85 584 


9. 99 999 


20 


40 


8. 00 363 


8. 00 365 


9. 99 998 


20 


50 


7. 85 876 


7. 85 877 


9. 99 999 


10 


50 


8.00 571 


8.00 574 


9. 99 998 


10 


250 


7. 86 166 


7. 86 167 


9. 99 999 


35 


35 


8. 00 779 


8. 00 781 


9. 99 998 


25 


10 


7. 86 455 


7. 86 456 


9. 99 999 


50 


10 


8. 00 985 


8. 00 987 


9. 99 998 


50 


20 


7. 86 741 


7. 86 743 


9. 99 999 


40 


20 


8. 01 190 


8. 01 193 


9. 99 998 


40 


30 


7. 87 026 


7. 87 027 


9. 99 999 


30 


30 


8. 01 395 


8. 01 397 


9. 99 998 


30 


40 


7. 87 309 


7.87 310 


9. 99 999 


20 


40 


8. 01 598 


8. 01 600 


9. 99 998 


20 


50 


7. 87 590 


7. 87 591 


9. 99 999 


10 


50 


8. 01 801 


8. 01 803 


9. 99 998 


10 


260 


7:87 870 


7. 87 871 


9. 99 999 


34 


36 


S. 02 002 


8. 02 004 


9. 99 998 


24 


10 


7. SS 147 


7. 88 148 


9. 99 999 


50 


10 


8. 02 203 


8. 02 205 


9. 99 998 


50 


20 


7. SS 423 


7. SS 424 


9. 99 999 


40 


20 


S. 02 402 


8. 02 405 


9. 99 998 


40 


30 


7. 88 697 


7. S8 698 


9. 99 999 


30 


30 


8. 02 601 


8. 02 604 


9. 99 998 


30 


40 


7. SS 969 


7. 88 970 


9. 99 999 


20 


40 


8. 02 799 


8. 02 801 


9. 99 998 


20 


50 


7. 89 240 


7. 89 241 


9. 99 999 


10 


50 


8. 02 996 


8. 02 998 


9. 99 998 


10 


270 


7. S9 509 


7.89 510 


9. 99 999 


33 


37 


8. 03 192 


8. 03 194 


9. 99 997 


23 


10 


7. S9 776 


7. 89 777 


9. 99 999 


50 


10 


8. 03 387 


8. 03 390 


9. 99 997 


50 


20 


7. 90 041 


7. 90 043 


9. 99 999 


40 


20 


8 03 581 


8. 03 5S4 


9. 99 997 


40 


30 


7. 90 305 


7. 90 307 


9. 99 999 


30 


30 


8. 03 775 


8. 03 777 


9. 99 997 


30 


40 


7. 90 568 


7. 90 569 


9. 99 999 


20 


40 


8. 03 967 


8. 03 970 


9. 99 997 


20 


50 


7. 90 829 


7. 90 S30 


9. 99 999 


10 


50 


8. 04 159 


8. 04 162 


9. 99 997 


10 


280 


7. 91 088 


7. 91 0S9 


9. 99 999 


32 


38 


8. 04 350 


8. 04 353 


9. 99 997 


22 


10 


7. 91 346 


7. 91 347 


9. 99 999 


50 


10 


S. 04 540 


8. 04 543 


9. 99 997 


50 


20 


7. 91 602 


7. 91 603 


9. 99 999 


40 


20 


8. 04 729 


8. 04 732 


9. 99 997 


40 


30 


7.91857 


7. 91 858 


9. 99 999 


30 


30 


S. 04 918 


8. 04 921 


9. 99 997 


30 


40 


7.92 110 


7.92111 


9. 99 998 


20 


40 


8. 05 105 


8. 05 10S 


9. 99 997 


20 


50 


7. 92 362 


7. 92 363 


9. 99 998 


10 


50 


8. 05 292 


8. 05 295 


9. 99 997 


10 


290 


7. 92 612 


7. 92 613 


9. 99 998 


031 


39 


8. 05 478 


8. 05 481 


9. 99 997 


021 


10 


7. 92 S61 


7. 92 862 


9. 99 998 


50 


10 


8. 05 663 


S. 05 666 


9. 99 997 


50 


20 


7. 93 10S 


7.93 110 


9. 99 998 


40 


20 


8. 05 848 


8.05 851 


9. 99 997 


40 


30 


7. 93 354 


7. 93 356 


9. 99 998 


30 


30 


8.06 031 


8. 06 034 


9. 99 997 


30 


40 


7. 93 599 


7. 93 601 


9. 99 99S 


20 


40 


8. 06 214 


S. 06 217 


9. 99 997 


20 


50 


7. 93 842 


7. 93 844 


9. 99 998 


10 


50 


8. 06 396 


S. 06 399 


9. 99 997 


10 


30 


7. 94 084 
log cos 


7. 94 086 


9. 99 99S 


30 


40 


8.06 578 


8. 06 581 


9. 99 997 


20 


t tt 


log cot 


log sin 


tt t 


r ft 


log cos 


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24 











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log sin 


log tan 


log COS 


tt J 


t tt 


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20 


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40 


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40 


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30 


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20 


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20 


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10 


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40 


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40 


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30 


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20 


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20 


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5 


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50 


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50 


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9. 99 996 


40 


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8. 20 675 


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40 


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30 


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30 


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20 


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20 


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10 


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4 


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40 


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40 


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30 


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30 


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20 


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20 


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10 


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3 


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50 


20 


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40 


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8.22 217 


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40 


30 


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30 


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30 


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20 


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20 


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2 


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t it 


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50 


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40 


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20 


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58 


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50 


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50 


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10 


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it t 


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27 


f tt 


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20 


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6 


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10 


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10 


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10 


49 


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1 


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30 


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20 


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20 


50 


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10 


50 


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10 


50 


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60 


8. 54 282 


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t tt 


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/ /' 


log cos 


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m 



28 




1° 






f 


log sin 


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t 




8 


8 


11 


9 








241S6 


24 192 


75 SOS 


99 993 


60 


1 


24 903 


24 910 


75 090 


99 993 


59 


2 


25 609 


25 616 


74 3S4 


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3 


26 304 


26 312 


73 6SS 


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57 


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26 9SS 


26 996 


73 004 


99 992 


56 


5 


27 661 


27 669 


72 331 


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55 


6 


2S324 


28 332 


7166S 


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54 


7- 


2S977 


2S9S6 


71014 


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53 


S 


29 621 


29 629 


70 371 


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52 


9 


30 255 


30 263 


69 737 


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51 


10 


30S79 


30SSS 


69112 


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50 


11 


31495 


31 505 


6S495 


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49 


12 


32103 


32112 


67SSS 


99 990 


4S 


13 


32 702 


32 711 


67 2S9 


99 990 


47 


14 


33 292 


33 302 


66 69S 


99 990 


46 


15 


33 S75 


33 SS6 


66114 


99 990 


45 


16 


34 450 


34 461 


65 539 


99 9S9 


44 


17 


35 018 


35 029 


64 971 


99 9S9 


43 


IS 


35 57S 


35 590 


64 410 


99 9S9 


42 


19 


36131 


36 143 


63S57 


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41 


20 


36 67S 


36 6S9 


63 311 


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40 


21 


37 217 


37 229 


62 771 


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39 


22 


37 750 


37 762 


62 23S 


99 9S8 


3S 


23 


3S276 


3S2S9 


61711 


99 9S7 


37 


24 


3S796 


3SS09 


61191 


99 9S7 


36 


25 


39 310 


39 323 


60 677 


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35 


26 


39 81S 


39S32 


6016S 


99 9S6 


34 


27 


40 320 


40 334 


59 666 


99 9S6 


33 


2S 


40S16 


40S30 


59170 


99 9S6 


32 


29 


41307 


41321 


5S679 


99 9S5 


31 


30 


41792 


41S07 


58 193 


99 9S5 


30 


31 


42 272 


42 2S7 


57 713 


99 985 


29 


32 


42 746 


42 762 


57 23S 


99 9S4 


2S 


33 


43 216 


43 232 


56 76S 


99 9S4 


27 


34 


43 6S0 


43 696 


56 304 


99 9S4 


26 


35 


44139 


44 156 


55S44 


99 983 


25 


36 


44 594 


44 611 


55 3S9 


99 9S3 


24 


37 


45 044 


45 061 


54 939 


99 9S3 


23 


3S 


45 4S9 


45 507 


54493 


99 9S2 


22 


39 


45 930 


45 94S 


54 052 


99 9S2 


21 


40 


46 366 


46 3S5 


53 615 


99 9S2 


20 


41 


46 799 


46817 


53 1S3 


99 9S1 


19 


42 


47 226 


47 245 


52 755 


99 9S1 


IS 


43 


47 650 


47 669 


52 331 


99 9S1 


17 


44 


4S069 


4S0S9 


51911 


99 9S0 


16 


45 


4S 4S5 


4S505 


51495 


99 9S0 


15 


46 


4SS96 


4S917 


510S3 


99 979 


14 


47 


49 304 


49 325 


50 675 


99979 


13 


4S 


49 70S 


49 729 


50 271 


99 979 


12 


49 


50 10S 


50130 


49S70 


99 97S 


11 


50 


50 504 


50 527 


49 473 


99 97S 


10 


51 


50 S97 


50 920 


49 0S0 


99 977 


9 


52 


51 2S7 


51310 


4S690 


99 977 


S 


53 


51 673 


51696 


4S304 


99 977 


- 7 


54 


52 055 


52 079 


47 921 


99 976 


6 


55 


52 434 


52 459 


47 541 


99 976 


5 


56 


52 S10 


52S35 


47165 


99 975 


4 


57 


53 1S3 


53 20S 


46 792 


99 975 


3 


58 


53 552 


53 57S 


46 422 


99 974 


2 


59 


53 919 


53 945 


46 055 


99 974 


1 


60 


54 2S2 


54 30S 


45 692 


99 974 







8 

log cos 


8 

log cot 


11 

log tan 


9 

log sin" 




t 


t 







2 


o 






t 


log sin 


log tan 


log cot 


log cos 


/ 




8 

54 2S2 


8 

54 30S 


11 

45 692 


9 

99 974 







60 


1 


54 642 


54 669 


45 331 


99 973 


59 


2 


54 999 


55 027 


44 973 


99 973 


58 


3 


55 354 


55 3S2 


44 61S 


99 972 


57 


4 


55 705 


55 734 


44 266 


99 972 


56 


5 


56 054 


56 0S3 


43 917 


99 971 


55 


6 


56 400 


56 429 


43 571 


99 971 


54 


7 


56 743 


56 773 


43 227 


99 970 


53 


S 


57 0S4 


57 114 


42SS6 


99 970 


52 


9 


57 421 


57 452 


42 54S 


99 969 


51 


10 


57 757 


57 7SS 


42 212 


99 969 


50 


11 


5S 0S9 


58 121 


41 879 


99 96S 


49 


12 


58 419 


58 451 


41 549 


99 96S 


4S 


13 


58 747 


5S779 


41221 


99 967 


47 


14 


59 072 


59 105 


40S95 


99 967 


46 


15 


59 395 


59 428 


40 572 


99 967 


45 


16 


59 715 ' 


59 749 


40 251 


99 966 


44 


17 


60 033 


60 068 


39 932 


99 966 


43 


IS 


60 349 


60 3S4 


39 616 


99 965 


42 


19 


60 662 


60 69S 


39 302 


99 964 


41 


20 


60 973 


61009 


3S991 


99 964 


40 


21 


612S2 


61319 


3S6S1 


99 963 


39 


22 


61 589 


61626 


3S 374 


99 963 


3S 


23 


61S94 


61931 


3S069 


99 962 


37 


24 


62196 


62 234 


37 766 


99 962 


36 


25 


62 497 


62 535 


37 465 


99 961 


35 


26 


62 795 


62S34 


37166 


99 961 


34 


27 


63 091 


63 131 


36S69 


99 960 


33 


2S 


63 3S5 


63 426 


36 574 


99 960 


32 


29 


6S67S 


63 71S 


36 2S2 


99 959 


31 


30 


63 96S 


64 009 


35 991 


99 959 


30 


31 


64 256 


64 29S 


35 702 


99 95 S 


29 


32 


64 543 


64 5S5 


35 415 


99 95S 


2S 


33 


64 827 


64 870 


35 130 


99 957 


27 


34 


65 110 


65 154 


34S46 


99 956 


26 


35 


65 391 


65 435 


34 565 


99 956 


25 


36 


65 670 


65 715 


34 2S5 


99 955 


24 


37 


65 947 


65 993 


34 007 


99 955 


23 


3S 


66 223 


66 269 


33 731 


99 954 


22 


39 


66 497 


66 543 


33 457 


99 954 


21 


40 


66 769 


66S16 


331S4 


99 953 


20 


41 


67 039 


67 0S7 


32 913 


99 952 


19 


42 


67 30S 


67 356 


32 644 


99 952 


IS 


43 


67 575 


67 624 


32 376 


99 951 


17 


44 


67S41 


67S90 


32110 


99 951 


16 


45 


6S104 


6S 154 


31S46 


99 950 


15 


46 


6S367 


6S417 


31 5S3 


99 949 


14 


47 


6S627 


6S67S 


31322 


99 949 


13 


4S 


6SSS6 


6S93S 


31062 


99 94S 


12 


49 


69144 


69196 


30S04 


99 94S 


11 


50 


69 400 


69 453 


30 547 


99 947 


10 


51 


69 654 


69 70S 


30 292 


99 946 


9 


52 


69 907 


69 962 


30 03S 


99 946 


S 


53 


70 159 


70 214 


29 7S6 


99 945 


7 


54 


70 409 


70 465 


29 535 


99 944 


6 


55 


70 65S 


70 714 


29 2S6 


99 944 


5 


56 


70 905 


70 962 


29 03S 


99 943 


4 


57 


71151 


7120S 


2S792 


99 942 


3 


58 


71395 


71453 


2S547 


99 942 


2 


59 


7163S 


71697 


2S303 


99 941 


1 


60 


71SS0 


71940 


2S060 


99 940 







8 


8 


11 


9 






t 


log cos 


log cot 


log tan 


log sin 


r 



88 



87 ; 







S 


o 






f 


log sin 


log tan 


log cot 


log cos 


r 




8 

71SS0 


8 

71940 


11 

28 060 


9 

99 940 







60 


1 


72 120 


72 1S1 


27 819 


99 940 


59 


2 


72 359 


72 420 


27 580 


99 939 


5S 


3 


72 597 


72 659 


27 341 


99 938 


57 


4 


72S34 


72 896 


27 104 


99 938 


56 


5 


73 069 


73 132 


26S6S 


99 937 


55 


6 


73 303 


73 366 


26 634 


99 936 


54 


7- 


73 535 


73 600 


26 400 


99 936 


53 


8 


73 767 


73 832 


26168 


99 935 


52 


9 


73 997 


74 063 


25 937 


99 934 


51 


10 


74 226 


74 292 


25 708 


99 934 


50 


11 


74 454 


74 521 


25 479 


99 933 


49 


12 


74 680 


74 748 


25 252 


99 932 


4S 


13 


74 906 


74 974 


25 026 


99 932 


47 


1+ 


75 130 


75199 


24 SOI 


99 931 


46 


15 


75 353 


75 423 


24 577 


99 930 


45 


16 


75 575 


75 645 


24 355 


99 929 


44 


17 


75 795 


75 867 


24133 


99 929 


43 


18 


76 015 


76 087 


23 913 


99 928 


42 


19 


76 234 


76 306 


23 694 


99 927 


41 


20 


76 451 


76 525 


23 475 


99 926 


40 


21 


76 667 


76 742 


23 258 


99 926 


39 


22 


76 883 


76 95S 


23 042 


99 925 


38 


23 


77 097 


77 173 


22 827 


99 924 


37 


24 


77 310 


77 387 


22 613 


99 923 


36 


25 


77 522 


77 600 


22 400 


99 923 


35 


26 


77 733 


77 811 


22 189 


99 922 


34 


27 


77 943 


7S022 


21978 


99 921 


33 


2S 


7S152 


78 232 


2176S 


99 920 


32 


29 


78 360 


78 441 


21559 


99 920 


31 


30 


78 568 


78 649 


21351 


99 919 


30 


31 


78 774 


78S55 


21145 


99 91S 


29 


32 


78 979 


79 061 


20 939 


99 917 


28 


33 


79183 


79 266 


20 734 


99 917 


27 


34 


79 386 


79 470 


20 530 


99 916 


26 


35 


79 5SS 


79 673 


20 327 


99 915 


25 


36 


79 789 


79 875 


20125 


99 914 


24 


37 


79 990 


SO 076 


19 924 


99 913 


23 


38 


SO 189 


80 277 


19 723 


99 913 


22 


39 


80 38S 


80 476 


19 524 


99 912 


21 


40 


80 585 


80 674 


19 326 


99 911 


20 


41 


80 782 


80S72 


19128 


99 910 


19 


42 


80 978 


81068 


18 932 


99 909 


18 


43 


SI 173 


81264 


IS 736 


99 909 


17 


44 


81367 


81459 


18 541 


99 90S 


16 


45 


81560 


81653 


18 347 


99 907 


15 


46 


81752 


SI 846 


18 154 


99 906 


14 


47 


SI 944 


82 038 


17 962 


99 905 


13 


48 


82134 


82 230 


17 770 


99 904 


12 


49 


S2 324 


82 420 


17 580 


99 904 


11 


50 


S2 513 


82 610 


17 390 


99 903 


10 


51 


S2 701 


82 799 


17 201 


99 902 


9 


52 


82 8SS 


82 987 


17 013 


99 901 


8 


53 


83 075 


S3 175 


16 825 


99 900 


7 


54 


83 261 


83 361 


16 639 


99 899 


6 


55 


83 446 


83 547 


16 453 


99 898 


5 


56 


83 630 


S3 732 


16 26S 


99 898 


4 


57 


83 813 


83 916 


16 084 


99 897 


3 


58 


83 996 


84 100 


15 900 


99S96 


2 


59 


84177 


84 282 


15 718 


99 895 


1 


60 


84 358 


84 464 


15 536 


99 894 


O 




8 

log cos 


8 

log cot 


11 

log tan 


9 

log sin 




t 


t 







4° 




29 


r 


log sin 


log tan 


log cot 


log cos 


t 




8 

S4 35S 


8 

84 464 


11 

15 536 


9 

99 894 







60 


1 


84 539 


S4 646 


15 354 


99 893 


59 


2 


84 718 


S4S26 


15 174 


99 892 


58 


3 


84 897 


S5 006 


14 994 


99 S91 


57 


4 


85 075 


S5 1S5 


14 815 


99 S91 


56 


5 


85 252 


S5 363 


14 637 


99 890 


55 


6 


85 429 


85 540 


14 460 


99 889 


54 


7 


85 605 


85 717 


14 283 


99 888 


53 


8 


85 780 


85 893 


14 107 


99 887 


52 


9 


S5 955 


86 069 


13 931 


99 886 


51 


10 


86128 


86 243 


13 757 


99 885 


50 


11 


86 301 


86 417 


13 583 


99 884 


49 


12 


S6 474 


86 591 


13 409 


99 883 


48 


13 


86 645 


86 763 


13 237 


99 882 


47 


14 


86 816 


86 935 


13 065 


99S81 


46 


15 


86 987 


87106 


12 894 


99,880 


45 


16 


87 156 


87 277 


12 723 


99 879 


44 


17 


87 325 


87 447 


12 553 


99S79 


43 


18 


87 494 


S7 616 


12 384 


99 878 


42 


19 


87 661 


87 785 


12 215 


99S77 


41 


20 


S7S29 


87 953 


12 047 


99 876 


40 


21 


87 995 


88 120 


11 880 


99 875 


39 


22 


88 161 


88 2S7 


11713 


99 874 


38 


23 


88 326 


88 453 


11547 


99 873 


37 


24 


S8 490 


SS618 


11382 


99 872 


36 


25 


8S654 


88 783 


11217 


99 871 


35 


26 


88 817 


88 948 


11052 


99 870 


34 


27 


88 980 


89111 


10SS9 


99S69 


33 


28 


89142 


S9 274 


10 726 


99 868 


32 


29 


89 304 


89 437 


10 563 


99 867 


31 


30 


89 464 


89 598 


10 402 


99S66 


30 


31 


89 625 


89 760 


10 240 


99 865 


29 


32 


89 784 


S9 920 


10 080 


99 864 


28 


33 


S9 943 


90 080 


09 920 


99 863 


27 


34 


90 102 


90 240 


09 760 


99 862 


26 


35 


90 260 


90 399 


09 601 


99 861 


25 


36 


90 417 


90 557 


09 443 


99 860 


24 


37 


90 574 


90 715 


09 285 


99 859 


23 


3S 


90 730 


90 872 


09128 


99 85S 


22 


39 


90 885 


91029 


08 971 


99 857 


21 


40 


91040 


91185 


08 815 


99 856 


20 


41 


91195 


91340 


08 660 


99S55 


19 


42 


91349 


91495 


08 505 


99 854 


18 


43 


91502 


91 650 


08 350 


99 853 


17 


44 


91655 


91803 


08197 


99 852 


16 


45 


91807 


91957 


08 043 


99 851 


15 


46 


91959 


92 110 


07 S90 


99 850 


14 


47 


92 110 


92 262 


07 738 


99S4S 


13 


48 


92 261 


92 414 


07 586 


99 847 


12 


49 


92 411 


92 565 


07 435 


99 846 


11 


50 


92 561 


92 716 


07 284 


99 845 


10 


51 


92 710 


92 866 


07 134 


99 844 


9 


52 


92 859 


93 016 


06 984 


99 843 


8 


53 


93 007 


93 165 


06 835 


99 842 


7 


54 


93154 


93 313 


06 687 


99 841 


6 


55 


93 301 


93 462 


06 538 


99 840 


5 


56 


93 448 


93 609 


06 391 


99 839 


4 


57 


93 594 


93 756 


06 244 


99 838 


3 


58 


93 740 


93 903 


06 097 


99 837 


2 


59 


93SS5 


94 049 


05 951 


99 836 


1 


60 


94 030 


94195 


05 80i 


99 834 







8 

log cos 


8 

log cot 


11 

log tan 


9 

log sin 




f 


t 



86 c 



85 



30 




5 


O 






r 


log sin 


log tan 


log cot 


log cos 


t 




8 


8 


11 


9 




O 


94 030 


94 195 


05 805 


99 834 


60 


1 


94174 


94 340 


05 660 


99 833 


59 


2 


94 317 


94 485 


05 515 


99 832 


5S 


3 


94 461 


94 630 


05 370 


99 831 


57 


-4 


94 603 


94 773 


05 227 


99 830 


56 


5 


94 746 


94 917 


05 083 


99 829 


55 


6 


94 887 


95 060 


04 940 


99 828 


54 


7 


95 029 


95 202 


04 798 


99 827 


53 


8 


95 170 


95 344 


04 656 


99 825 


52 


9 


95 310 


95 486 


04 514 


99 824 


51 


10 


95 450 


95 627 


04 373 


99 823 


50 


11 


95 589 


95 767 


04 233 


99 822 


49 


12 


95 728 


95 908 


04 092 


99 821 


48 


13 


95 867 


96 047 


03 953 


99 820 


47 


14 


96 005 


96187 


03 813 


99 819 


46 


15 


96143 


96 325 


03 675 


99 817 


45 


16 


96 280 


96 464 


03 536 


99 816 


44 


17 


96 417 


96 602 


03 398 


99 815 


43 


18 


96 553 


96 739 


03 261 


99 814 


42 


19 


96 689 


96 877 


03 123 


99 813 


41 


20 


96 825 


97 013 


02 987 


99 812 


40 


21 


96 960 


97150 


02 850 


99 810 


39 


22 


97 095 


97 285 


02 715 


99 809 


38 


23 


97 229 


97 421 


02 579 


99 808 


37 


24 


97 363 


97 556 


02 444 


99 807 


36 


25 


97 496 


97 691 


02 309 


99 806 


35 


26 


97 629 


97 825 


02 175 


99 804 


34 


27 


97 762 


97 959 


02 041 


99 803 


33 


28 


97 894 


98 092 


01908 


99 802 


32 


29 


98 026 


98 225 


01775 


99 801 


31 


30 


98157 


98 358 


01642 


99 800 


30 


31 


98 288 


98 490 


01510 


99 798 


29 


32 


98 419 


98 622 


01378 


99 797 


28 


33 


98 549 


98 753 


01247 


99 796 


27 


34 


98 679 


98 884 


01116 


99 795 


26 


35 


98 808 


99 015 


00 985 


99 793 


25 


36 


98 937 


99145 


00 855 


99 792 


24 


37 


99 066 


99 275 


00 725 


99 791 


23 


38 


99194 


99 405 


00 595 


99 790 


22 


39 


99 322 


99 534 


00 466 


99 788 


21 


40 


99 450 


99 662 


00 338 


99 787 


20 


41 


99 577 


99 791 


00 209 


99 786 


19 


42 


99 704 


99 919 


00 081 


99 785 


18 


43 


99 830 


00 046 


99 9^4 


99 783 


17 


44 


99 956 


00174 


99 826 


99 782 


16 


45 


00 082 


00 301 


99 699 


99 781 


15 


46 


00 207 


00 427 


99 573 


99 780 


14 


47 


00 332 


00 553 


99 447 


99 778 


13 


48 


00 456 


00 679 


99 321 


99 777 


12 


49 


00 5S1 


00 805 


99195 


99 776 


11 


50 


00 704 


00 930 


99 070 


99 775 


10 


51 


00 828 


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98 945 


99 773 


9 


52 


00 951 


01179 


98 821 


99 772 


8 


53 


01074 


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98 697 


99 771 


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54 


01196 


01427 


98 573 


99 769 


6 


55 


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01550 


98 450 


99 768 


5 


56 


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01673 


98 327 


99 767 


4 


57 


01561 


01796 


98 204 


99 765 


3 


58 


01682 


01918 


98 082 


99 764 


2 


59 


01803 


02 040 


97 960 


99 763 


1 


60 


01923 


02 162 


97 838 


99 761 







9 


9 


10 


9 




t 


log COS 


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t 


log sin 


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/ 




9 

01923 


9 • 

02 162 


io 

97 83S 


9 

99 761 




o 


60 


1 


02 043 


02 283 


97 717 


99 760 


59 


2 


02 163 


02 404 


97 596 


99 759 


58 


3 


02 283 


02 525 


97 475 


99 757 


57 


4 


02 402 


02 645 


97 355 


99 756 


56 


5 


02 520 


02 766 


97 234 


99 755 


55 


6 


02 639 


02 885 


97115 


99 753 


54 


7 


02 757 


03 005 


96 995 


99 752 


53 


8 


02 874 


03 124 


96 876 


99 751 


52 


9 


02 992 


03 242 


96 758 


99 749 


51 


10 


03 109 


03 361 


96 639 


99 748 


50 


11 


03 226 


03 479 


96 521 


99 747 


49 


12 


03 342 


03 597 


96 403 


99 745 


48 


13 


03 458 


03 714 


96 286 


99 744 


47 


14 


03 574 


03 832 


96168 


99 742 


46 


15 


03 690 


03 948 


96 052 


99 741 


45 


16 


03 805 


04 065 


95 935 


99 740 


44 


17 


03 920 


04 181 


95 819 


99 738 


43 


18 


04 034 


04 297 


95 703 


99 737 


42 


19 


04 149 


04 413 


95 587 


99 736 


41 


20 


04 262 


04 528 


95 472 


99 734 


40 


21 


04 376 


04 643 


95 357 


99 733 


39 


22 


04 490 


04 75S 


95 242 


99 731 


38 


23 


04 603 


04 873 


95 127 


99 730 


37 


24 


04 715 


04 987 


95 013 


99 728 


36 


25 


04 82S 


05 101 


94 899 


99 727 


35 


26 


04 940 


05 214 


94 786 


99 726 


34 


27 


05 052 


05 328 


94 672 


99 724 


33 


28 


05 164 


05 441 


94 559 


99 723 


32 


29 


05^75 


05 553 


94 447 


99 721 


31 


30 


05'386 


05 666 


94 334 


99 720 


30 


31 


05 497 


05 778 


94 222 


99 718 


29 


32 


05 607 


05 890 


94 110 


99 717 


28 


33 


05 717 


06 002 


93 998 


99 716 


27 


34 


05 827 


06113 


93 887 


99 714 


26 


35 


05 937 


06 224 


93 776 


99 713 


25 


36 


06 046 


06 335 


93 665 


99 711 


24 


37 


06155 


06 445 


93 555 


99 710 


23 


38 


06 264 


06 556 


93 444 


99 708 


22 


39 


06 372 


06 666 


93 334 


99 707 


21 


40 


06 481 


06 775 


93 225 


99 705 


20 


41 


06 589 


06 885 


93 115 


99 704 


19 


42 


06 696 


06 994 


93 006 


99 702 


18 


43 


06 804 


07 103 


92 897 


99 701 


17 


44 


06 911 


07 211 


92 789 


99 699 


16 


45 


07 018 


07 320 


92 680 


99 698 


15 


46 


07 124. 


07 428 


92 572 


99 696 


14 


47 


07 231 


07 536 


92 464 


99 695 


13 


48 


07 337 


07 643 


92 357 


99 693 


12 


49 


07 442 


07 751 


92 249 


99 692 


11 


50 


07 548 


07 858 


92142 


99 690 


10 


51 


07 653 


07 964 


92 036 


99 689 


9 


52 


07 758 


08 071 


91929 


99 687 


8 


53 


07 863 


08 177 


91823 


99 686 


7 


54 


07 968 


08 283 


91717 


99 684 


6 


55 


08 072 


08 389 


91611 


99 683 


5 


56 


08 176 


08 495 


91 505 


99 681 


4 


57 


08 280 


08 600 


91400 


99 680 


3 


58 


08 383 


08 705 


91 295 


99 678 


2 


59 


0S4S6 


0SS10 


91190 


99 677 


1 


60 


08 589 


08 914 


91086 


99 675 


O 




9 

log cos 


9 

log cot 


10 

log tan 


9 

log sin 




t 


t 



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83 c 







7 


o 






r 


log sin 


log tan 


log cot 


log cos 


t 




9 

OS 589 


9 

08 914 


10 

91086 


9 

99 675 







60 


1 


08 692 


09 019 


90 981 


99 674 


59 


2 


OS 795 


09123 


90 877 


99 672 


5S 


3 


OS 897 


09 227 


90 773 


99 670 


57 


4 


OS 999 


09 330 


90 670 


99 669 


56 


5 


09101 


09 434 


90 566 


99 667 


55 


6 


09 202 


09 537 


90 463 


99 666 


54 


7 


09 304 


09 640 


90 360 


99 664 


53 


8 


09 405 


09 742 


90 258 


99 663 


52 


9 


09 506 


09 845 


90155 


99 661 


51 


io 


09 606 


09 947 


90 053 


99 659 


50 


11 


09 707 


10 019 


89 951 


99 65S 


49 


12 


09 807 


10150 


89 850 


99 656 


48 


13 


09 907 


10 252 


89 748 


99 655 


47 


14 


10 006 


10 353 


89 647 


99 653 


46 


15 


10106 


10 454 


89 546 


99 651 


45 


16 


10 205 


10 555 


89 445 


99 650 


44 


17 


10 304 


10 656 


89 344 


99 64S 


43 


18 


10 402 


10 756 


89 244 


99 647 


42 


19 


10 501 


10 856 


89144 


99 645 


41 


20 


10 599 


10 956 


89 044 


99 643 


40 


21 


10 697 


11056 


88 944 


99 642 


39 


22 


10 795 


11 155 


88 845 


99 640 


38 


23 


10S93 


11254 


88 746 


99 638 


37 


24 


10 990 


11353 


88 647 


99 637 


36 


25 


11087 


11452 


8S548 


99 635 


35 


26 


11184 


11551 


88 449 


99 633 


34 


27 


11281 


11649 


SS351 


99 632 


33 


' 28 


11377 


11747 


88 253 


99 630 


32 


29 


11474 


11845 


88155 


99 629 


31 


30 


11570 


11943 


88 057 


99 627 


30 


31 


11666 


12 0+0 


87 960 


99 625 


29 


32 


11761 


12 138 


87 862 


99 624 


28 


33 


11857 


12 235 


87 765 


99 622 


27 


34 


11952 


12 332 


87 668 


99 620 


26 


35 


12 047 


12 428 


87 572 


99 618 


25 


36 


"12 142 


12 525 


87 475 


99 617 


24 


37 


12 236 


12 621 


S7 379 


99 615 


23 


3S 


12 331 


12 717 


87 283 


99 613 


22 


39 


12 425 


12 813 


87 187 


99 612 


21 


40 


12 519 


12 909 


87 091 


99 610 


20 


41 


12 612 


13 004 


86 996 


99 60S 


19 


42 


12 706 


13 099 


86 901 


99 607 


18 


43 


12 799 


13 194 


86 806 


99 605 


17 


44 


12 892 


13 289 


86 711 


99 603 


16 


45 


12 985 


13 384 


86 616 


99 601 


15 


46 


13 078 


13 478 


86 522 


99 600 


14 


47 


13 171 


13 573 


86 427 


99 598 


13 


48 


13 263 


13 667 


86 333 


99 596 


12 


49 


13 355 


13 761 


86 239 


99 595 


11 


50 


13 447 


13 854 


86146 


99 593 


IO 


51 


13 539 


13 948 


86 052 


99 591 


9 


52 


13 630 


14 0+1 


85 959 


99 589 


8 


53 


13 722 


14 134 


85 866 


99 588 


7 


54 


13 813 


14 227 


85 773 


99 586 


6 


55 


13 904 


14 320 


85 6S0 


99 584 


5 


56 


13 994 


14 412 


85 58S 


99 582 


4 


57 


14 085 


14 50+ 


85 496 


99 581 


3 


58 


14 175 


14 597 


85 403 


99 579 


2 


59 


14 266 


14 688 


85 312 


99 577 


1 


60 


14 356 


14 780 


85 220 


99 575 


O 




9 

log cos 


9 

log cot 


IO 

log tan 


9 

log sin 




t 


f 







8 


o 




31 


t 


log sin 


log tan 


log cot 


log cos 


r 




9 


9 


10 


9 




o 


14 356 


14 780 


85 220 


99 575 


60 


1 


14 445 


14 872 


85 128 


99 574 


59 


2 


14 535 


14 963 


85 037 


99 572 


5S 


3 


14 62+ 


15 054 


84 946 


99 570 


57 


4 


14 714 


15 145 


84 855 


99 568 


56 


5 


14 803 


15 236 


84 764 


99 566 


55 


6 


14 891 


15 327 


84 673 


99 565 


54 


7 


14 980 


15 417 


84 583 


99 563 


53 


S 


15 069 


15 508 


84 492 


99 561 


52 


9 


15 157 


15 598 


84 402 


99 559 


51 


10 


15 245 


15 688 


84 312 


99 557 


50 


11 


15 333 


15 777 


84 223 


99 556 


49 


12 


15 421 


15 867 


84133 


99 554 


48 


13 


15 50S 


15 956 


84 044 


99 552 


47 


14 


15 596 


16 046 


83 954 


99 550 


46 


15 


15 683 


16135 


83 865 


99 548 


45 


16 


15 770 


16 224 


83 776 


99 546 


44 


17 


15S57 


16 312 


83 688 


99 545 


43 


18 


15 944 


16 401 


83 599 


99 543 


42 


19 


16 030 


16 489 


83 511 


99 541 


41 


20 


16116 


16 577 


83 423 


99 539 


40 


21 


16 203 


16 665 


83 335 


99 537 


39 


22 


16 289 


16 753 


83 247 


99 535 


38 


23 


16 374 


16 841 


83 159 


99 533 


37 


24 


16 460 


16 928 


83 072 


99 532 


36 


25 


16 545 


17 016 


82 984 


99 530 


35 


26 


16 631 


17 103 


82 897 


99 528 


34 


27 


16 716 


17 190 


82 810 


99 526 


33 


2S 


16 801 


17 277 


82 723 


99 524 


32 


29 


16 886 


17 363 


82 637 


99 522 


31 


30 


16 970 


17 450 


82 550 


99 520 


30 


31 


17 055 


17 536 


82 464 


99 518 


29 


32 


17 139 


17 622 


82 378 


99 517 


28 


33 


17 223 


17 708 


82 292 


99 515 


27 


34 


17 307 


17 794 


82 206 


99 513 


26 


35 


17 391 


17 880 


82 120 


99 511 


25 


36 


17 474 


17 965 


82 035 


99 509 


24 


37 


17 558 


18 051 


81949 


99 507 


23 


38 


17 641 


18 136 


81864 


99 505 


22 


39 


17 724 


18 221 


81779 


99 503 


21 


40 


17 807 


18 306 


81694 


99 501 


20 


41 


17 890 


18 391 


81609 


99 499 


19 


42 


17 973 


18 475 


81525 


99 497 


18 


43 


18 055 


18 560 


81440 


99 495 


17 


44 


18137 


18 644 


81356 


99 494 


16 


45 


18 220 


18 728 


81272 


99 492 


15 


46 


18 302 


18 812 


811SS 


99 490 


14 


47 


1S3S3 


18 896 


81 104 


99 488 


13 


48 


18 465 


18 979 


81021 


99 486 


12 


49 


18 547 


19 063 


80 937 


99 484 


11 


50 


18 628 


19146 


80 854 


99 4S2 


10 


51 


18 709 


19 229 


80 771 


99 480 


9 


52 


18 790 


19 312 


80 688 


99 478 


8 


53 


18S71 


19 395 


80 605 


99 476 


7 


54 


18 952 


19 478 


80 522 


99 474 


6 


55 


19 033 


19 561 


80 439 


99 472 


5 


56 


19113 


19 643 


80 357 


99 470 


4 


57 


19193 


19 725 


80 275 


99 468 


3 


58 


19 273 


19 807 


80193 


99 466 


2 


59 


19 353 


19 889 


80 111 


99 464 


1 


60 


19 433 


19 971 


80 029 


99 462 







9 

log cos 


9 

log cot 


IO 

log tan 


9 

log sin 




r 


r 



82 



8r 



32 




9 









t 


log sin 


log tan 


log cot 


log cos 


/ 




9 


9 


10 


9 






o 


19 433 


19 971 


80 029 


99 462 


60 


1 


19 513 


20 053 


79 947 


99 460 


59 


2 


19 592 


20134 


79 866 


99 458 


58 


3 


19 672 


20 216 


79 784 


99 456 


57 


4' 


19 751 


20 297 


79 703 


99 454 


56 


5 


19 830 


20 378 


79 622 


99 452 


55 


6 


19 909 


20 459 


79 541 


99 450 


54 


7 


19 9S8 


20 540 


79 460 


99 448 


53 


8 


20 067 


20 621 


79 379 


99 446 


52 


9 


20145 


20 701 


79 299 


99 444 


51 


10 


20 223 


20 782 


79 218 


99 442 


50 


11 


20 302 


20 862 


79138 


99 440 


49 


12 


20 380 


20 942 


79 058 


99 438 


48 


13 


20 458 


21022 


78 978 


99 436 


47 


14 


20 535 


21102 


78 898 


99 434 


46 


15 


20 613 


21182 


78 818 


99 432 


45 


16 


20 691 


21261 


78 739 


99 429 


44 


17 


20 768 


21341 


78 659 


99 427 


43 


18 


20 845 


21420 


78 580 


99 425 


42 


19 


20 922 


21499 


78 501 


99 423 


41 


20 


20 999 


21578 


78 422 


99 421 


40 


21 


21076 


21657 


78 343 


99 419 


39 


22 


21153 


21736 


78 264 


99 417 


3S 


23 


21229 


21814 


78 186 


99 415 


37 


24 


21306 


21893 


78107 


99 413 


36 


25 


21382 


21971 


78 029 


99 411 


35 


26 


21458 


22 049 


77 951 


99 409 


34 


27 


21534 


22 127 


77 873 


99 407 


33 


28 


21610 


22 205 


77 795 


99 404 


32 


29 


21685 


22 2S3 


77 717 


99 402 


31 


30 


21761 


22 361 


77 639 


99 400 


30 


31 


21836 


22 438 


77 562 


99 398 


29 


32 


21912 


22 516 


77 484 


99 396 


28 


33 


21987 


22 593 


77 407 


99 394 


27 


34 


22 062 


22 670 


77 330 


99 392 


26 


35 


22137 


22 747 


77 253 


99 390 


25 


36 


22 211 


22 824 


77176 


99 388 


24 


37 


22 286 


22 901 


77 099 


99 385 


23 


38 


22 361 


22 977 


77 023 


99 383 


22 


39 


22 435 


23 054 


76 946 


99 381 


21 


40 


22 509 


23 130 


76 870 


99 379 


20 


41 


22 583 


23 206 


76 794 


99 377 


19 


42 


22 657 


23 283 


76 717 


99 375 


18 


43 


22 731 


23 359 


76 641 


99 372 


17 


44 


22 805 


23 435 


76 565 


99 370 


16 


45 


22 878 


23 510 


76 490 


99 368 


15 


46 


22 952 


23 5S6 


76 414 


99 366 


14 


47 


23 025 


23 661 


76 339 


99 364 


13 


48 


23 098 


23 737 


76 263 


99 362 


12 


49 


23171 


23 812 


76188 


99 359 


11 


50 


23 244 


23 887 


76113 


99 357 


IO 


51 


23 317 


23 962 


76 038 


99 355 


9 


52 


23 390 


24 037 


75 963 


99 353 


8 


53 


23 462 


24112 


75 888 


99 351 


7- 


54 


23 535 


24186 


75 814 


99 348 


6 


55 


23 607 


24 261 


75 739 


99 346 


5 


56 


23 679 


24 335 


75 665 


99 344 


4 


57 


23 752 


24 410 


75 590 


99 342 


3 


58 


23 823 


24 484 


75 516 


99 340 


2 


59 


23 895 


24 558 


75 442 


99 337 


1 


60 


23 967 


24 632 


75 368 


99 335 







9 

log cos 


9 

log cot 


io 

log tan 


9 

log sin 




t 


■f 



10 c 



t 


log sin 


log tan 


log cot 


log cos 


/ 




9 

23 967 


9 

24 632 


10 

75 368 


9 

99 335 




o 


60 


1 


24 039 


24 706 


75 294 


99 333 


59 


2 


24110 


24 779 


75 221 


99 331 


58 


3 


24 181 


24 853 


75 147 


99 328 


57 


4 


24 253 


24 926 


75 074 


99 326 


56 


5 


24 324 


25 000 


75 000 


99 324 


55 


6 


24 395 


25 073 


74 927 


99 322 


54 


7 


24 466 


25 146 


74 854 


99 319 


53 


8 


24 536 


25 219 


74 781 


99 317 


52 


9 


24 607 


25 292 


74 708 


99 315 


51 


IO 


24 677 


25 365 


74 635 


99 313 


50 


11 


24 748 


25 437 


74 563 


99 310 


49 


12 


24 818 


25 510 


74 490 


99 308 


48 


13 


24 888 


25 582 


74 418 


99 306 


47 


14 


24 958 


25 655 


74 345 


99 304 


46 


15 


25 028 


25 727 


74 273 


99 301 


45 


16 


25 098 


25 799 


74 201 


99 299 


44 


17 


25 168 


25 871 


74129 


99 297 


43 


18 


25 237 


25 943 


74 057 


99 294 


42 


19 


25 307 


26 015 


73 985 


99 292 


41 


20 


25 376 


26 086 


73 914 


99 290 


40 


21 


25 445 


26158 


73 842 


99 288 


39 


22 


25 514 


26 229 


73 771 


99 285 


38 


23 


25 583 


26 301 


73 699 


99 283 


37 


24 


25 652 


26 372 


73 628 


99 281 


36 


25 


25 721 


26 443 


73 557 


99 278 


35 


26 


25 790 


26 514 


73 486 


99 276 


34 


27 


25 858 


26 585 


73 415 


99 274 


33 


28 


25 927 


26 655 


73 345 


99 271 


32 


29 


25 995 


26 726 


73 274 


99 269 


31 


30 


26 06'3 


26 797 


73 203 


99 267 


30 


31 


26131 


26 867 


73 133 


99 264 


29 


32 


26199 


26 937 


73 063 


99 262 


28 


33 


26 267 


27 008 


72 992 


99 260 


27 


34 


26 335 


27 078 


72 922 


99 257 


26 


35 


26 403 


27148 


72 852 


99 255 


25 


36 


26 470 


27 218 


72 782 


99 252 


24 


37 


26 538 


27 28S 


72 712 


99 250 


23 


38 


26 605 


27 357 


72 643 


99 248 


22 


39 


26 672 


27 427 


72 573 


99 245 


21 


40 


26 739 


27 496 


72 504 


99 243 


20 


41 


26 806 


27 566 


72 434 


99 241 


19 


42 


26 873 


27 635 


72 365 


99 238 


18 


43 


26 940 


27 704 


72 296 


99 236 


17 


44 


27 007 


27 773 


72 227 


99 233 


16 


45 


27 073 


27 842 


72 158 


99 231 


15 


46 


27 140 


27 911 


72 089 


99 229 


14 


47 


27 206 


27 980 


72 020 


99 226 


13 


4S 


27 273 


28 049 


71951 


99 224 


12 


49 


27 339 


28117 


71883 


99 221 


11 


50 


27 405 


28186 


71814 


99 219 


IO 


51 


27 471 


28 254 


71746 


99 217 


9 


52 


27 537 


28 323 


71677 


99 214 


8 


53 


27 602 


28 391 


71609 


99 212 


7 


54 


27 668 


28 459 


71541 


99 209 


6 


55 


27 734 


28 527 


71473 


99 207 


5 


56 


27 799 


28 595 


71405 


99 204 


4 


57 


27 864 


28 662 


71338 


99 202 


3 


5S 


27 930 


28 730 


71270 


99 200 


2 


59 


27 995 


28 79S 


71202 


99197 


1 


60 


28 060 


28 865 


71135 


99 195 


O 




9 

log cos 


9 

log cot 


IO 

log tan 


9 

log sin 




t 


f 



80 c 



W 







ir 






t 


log sin 


log tan 


log cot 


log cos 


t 




9 

28 060 


9 

28 865 


10 

71135 


9 

99 195 







60 


1 


28 125 


2S933 


71067 


99 192 


59 


2 


28 190 


29 000 


71000 


99 190 


58 


3 


28 254 


29 067 


70 933 


99 187 


57 


4 


28 319 


29134 


70 866 


99 185 


56 


5 


2S3S4 


29 201 


70 799 


99 1S2 


55 


6 


28 448 


29 268 


70 732 


99 180 


54 


7 


2S512 


29 335 


70 665 


99177 


53 


8 


28 577 


29 402 


70 598 


99 175 


52 


9 


28 641 


29 46S 


70 532 


99 172 


51 


io 


2S705 


29 535 


70 465 


99170 


50 


11 


2S769 


29 601 


70 399 


99 167 


49 


12 


28 S33 


29 66S 


70 332 


99165 


4S 


13 


2SS96 


29 734 


70 266 


99 162 


47 


14 


2S960 


29 800 


70 200 


99160 


46 


15 


29 024 


29 866 


70134 


99 157 


45 


16 


29 0S7 


29 932 


70 068 


99 155 


44 


17 


29150 


29 99S 


70 002 


99 152 


43 


IS 


29 214 


30 064 


69 936 


99150 


42 


19 


29-277 


30130 


69 870 


99 147 


41 


20 


29 340 


30195 


69 805 


99 145 


40 


21 


29 403 


30 261 


69 739 


99 142 


39 


22 


29 466 


30 326 


69 674 


99 140 


38 


23 


29 529 


30 391 


69 609 


99 137 


37 


24 


29 591 


30 457 


69 543 


99135 


36 


25 


29 654 


30 522 


69 478 


99 132 


35 


26 


29 716 


30 587 


69 413 


99130 


34 


27 


29 779 


30 652 


69 348 


99 127 


33 


2S 


29 841 


30 717 


69 283 


99124 


32 


29 


29 903 


30 782 


69 218 


99122 


31 


30 


29 966 


30 846 


69154 


99119 


30 


31 


30 028 


30 911 


69 089 


99 117 


29 


32 


30 090 


30 975 


69 025 


99114 


28 


33 


30 151 


31040 


6S960 


99112 


27 


34 


30 213 


31104 


6SS96 


99109 


26 


35 


30 275 


31168 


68 832 


99 106 


25 


36 


"30 336 


31233 


68 767 


99104 


24 


37 


30 39S 


31297 


68 703 


99 101 


23 


38 


30 459 


31361 


68 639 


99 099 


22 


39 


30 521 


31425 


6S575 


99 096 


21 


40 


30 5S2 


31489 


6S511 


99 093 


20 


41 


30 643 


31552 


6S448 


99 091 


19 


42 


30 704 


31616 


6S3S4 


99 OSS 


18 


43 


30 765 


31679 


68 321 


99 0S6 


17 


44 


30 826 


31743 


6S257 


99 083 


16 


45 


30 887 


31S06 


6S194 


99 0S0 


15 


46 


30 947 


31870 


6S130 


99 078 


14 


47 


31008 


31933 


68 067 


99 075 


13 


4S 


31068 


31996 


6S004 


99 072 


12 


49 


31129 


32 059 


67 941 


99 070 


11 


50 


31189 


32122 


67 87S 


99 067 


10 


51 


31250 


32 185 


67 815 


99 064 


9 


52 


31310 


32 24S 


67 752 


99 062 


8 


53 


31370 


32311 


67 689 


99 059 


7 


54 


31430 


32 373 


67 627 


99 056 


6 


55 


31490 


32 436 


67 564 


99 054 


5 


56 


31549 


32 49S 


67 502 


99 051 


4 


57 


31609 


32 561 


67 439 


99 04S 


3 


5S 


31669 


32 623 


67 377 


99 046 


2 


59 


3172S 


32 685 


67 315 


99 043 


1 


60 


31788 


32 747 


67 253 


99 040 







9 

log COS 


9 

log cot 


10 

log tan 


9 

log sin 




f 


f 



12 c 



t 


log sin 


log tan 


log cot 


log cos 


t 




9 

31 7SS 


9 

32 747 


10 

67 253 


9 

99 040 







60 


1 


31847 


32 810 


67 190 


99 03S 


59 


2 


31 907 


32 872 


67 128 


99 035 


58 


3 


31966 


32 933 


67 067 


99 032 


57 


4 


32 025 


32 995 


67 005 


99 030 


56 


5 


32 0S4 


33 057 


66 943 


99 027 


55 


6 


32 143 


33 119 


66 881 


99 024 


54 


7 


32 202 


33 ISO 


66 820 


99 022 


53 


S 


32 261 


33 242 


66 758 


99 019 


52 


9 


32 319 


33 303 


66 697 


99 016 


51 


10 


32 37S 


33 365 


66 635 


99 013 


50 


11 


32 437 


33 426 


66 574 


99 011 


49 


12 


32 495 


33 4S7 


66 513 


99 008 


48 


13 


32 553 


33 548 


66 452 


99 005 


47 


14 


32 612 


33 609 


66 391 


99 002 


46 


15 


32 670 


33 670 


66 330 


99 000 


45 


16 


32 728 


33 731 


66 269 


9S997 


44 


17 


32 786 


33 792 


66 208 


9S994 


43 


IS 


32 844 


33 S53 


66 147 


98 991 


42 


19 


32 902 


33 913 


66 087 


9S9S9 


41 


20 


32 960 


33 974 


66 026 


98 986 


40 


21 


33 01S 


34 034 


65 966 


9S9S3 


39 


22 


33 075 


34 095 


65 905 


98 980 


38 


23 


33 133 


34155 


65 845 


98 978 


37 


24 


33 190 


34 215 


65 785 


98 975 


36 


25 


33 248 


34 276 


65 724 


98 972 


35 


26 


33 305 


34 336 


65 664 


98 969 


34 


27 


33 362 


34 396 


65 604 


98 967 


33 


28 


33 420 


34 456 


65 544 


98 964 


32 


29 


33 477 


34 516 


65 484 


9S961 


31 


30 


33 534 


34 576 


65 424 


98 95S 


30 


31 


33 591 


34 635 


65 365 


98 955 


29 


32 


33 647 


34 695 


65 305 


9S953 


28 


33 


33 704 


34 755 


65 245 


98 950 


27 


34 


33 761 


34 814 


65 186 


98 947 


26 


35 


33 SIS 


34 874 


65 126 


98 944 


25 


36 


33 874 


34 933 


65 067 


98 941 


24 


37 


33 931 


34 992 


65 008 


98 93S 


23 


38 


33 987 


35 051 


64 949 


98 936 


22 


39 


34 043 


35 111 


64 8S9 


98 933 


21 


40 


34 100 


35 170 


64 830 


9S930 


20 


41 


34 156 


35 229 


64 771 


98 927 


19 


42 


34 212 


35 288 


64 712 


98 924 


18 


43 


34 26S 


35 347 


64 653 


9S921 


17 


44 


34 324 


35 405 


64 595 


9S919 


16 


45 


34 380 


35 464 


64 536 


98 916 


15 


46 


34 436 


35 523 


64 477 


98 913 


14 


47 


34 491 


35 581 


64 419 


98 910 


13 


48 


34 547 


35 640 


64 360 


98 907 


12 


49 


34 602 


35 698 


64 302 


98 904 


11 


50 


34 65S 


35 757 


64 243 


98 901 


10 


51 


34 713 


35 815 


64 185 


98 898 


9 


52 


34 769 


35 873 


64 127 


98 896 


8 


53 


34S24 


35 931 


64 069 


9SS93 


7 


54 


34 879 


35 989 


64 011 


9SS90 


6 


55 


34 934 


36 047 


63 953 


98 887 


5 


56 


34 989 


36105 


63 895 


98 884 


4 


57 


35 044 


36163 


63 837 


9SSS1 


3 


5S 


35 099 


36 221 


63 779 


9SS78 


2 


59 


35 154 


36 279 


63 721 


98 875 


1 


60 


35 209 


36 336 


63 664 


9S872 


O 




9 


9 


IO 


9 




t 


log cos 


log cot 


log tan 


log sin 


i 



78 r 



7?t 



34 




13° 






r 


log sin 


log tan 


log cot 


log cos 


t 




9 


9 


io 


9 








O 


35 209 


36 336 


63 664 


9SS72 


60 


1 


35 263 


36 394 


63 606 


98S69 


59 


2 


35 318 


36 452 


63 548 


98S67 


58 


3 


35 373 


36 509 


63 491 


98 864 


57 


4 


35 427 


36 566 


63 434 


98 861 


56 


5 


35 481 


36 624 


63 376 


9S858 


55 


6 


35 536 


36 681 


63 319 


98 855 


54 


7 


35 590 


36 738 


63 262 


98 852 


53 


8 


35 644 


36 795 


63 205 


98 849 


52 


9 


35 69S 


36 852 


63 148 


98 846 


51 


10 


35 752 


36 909 


63 091 


98 843 


50 


11 


35 806 


36 966 


63 034 


9SS40 


49 


12 


35 860 


37 023 


62 977 


98 837 


4S 


13 


35 914 


37 080 


62 920 


98 834 


47 


14 


35 968 


37137 


62 863 


98 831 


46 


15 


36 022 


37193 


62 807 


98 828 


45 


16 


36 075 


37 250 


62 750 


98 825 


44 


17 


36129 


37 306 


62 694 


98 822 


43 


IS 


36182 


37 363 


62 637 


98 819 


42 


19 


36 236 


37 419 


62 581 


98 816 


41 


20 


36 289 


37 476 


62 524 


9S813 


40 


21 


36 342 


37 532 


62 468 


98 810 


39 


22 


36 395 


37 588 


62 412 


98 807 


38 


23 


36 449 


37 644 


62 356 


98 804 


37 


24 


36 502 


37 700 


62 300 


98 801 


36 


25 


36 555 


37 756 


62 244 


98 798 


35 


26 


36 608 


37 812 


62188 


98 795 


34 


27 


36 660 


37 868 


62132 


98 792 


33 


2S 


36 713 


37 924 


62 076 


98 789 


32 


29 


36 766 


37 980 


62 020 


98 786 


31 


30 


36 819 


38 035 


61965 


9S7S3 


30 


31 


36 871 


38 091 


61909 


98 780 


29 


32 


36 924 


38 147 


61853 


98 777 


28 


33 


36 976 


38 202 


61798 


98 774 


27 


34 


37 028 


38 257 


61743 


98 771 


26 


35 


37 081 


38 313 


61687 


9S 768 


25 


36 


37133 


38 368 


61632 


98 765 


24 


37 


37 1S5 


38 423 


61 577 


98 762 


23 


38 


37 237 


38 479 


61521 


9S759 


22 


39 


37 2S9 


38 534 


61466 


98 756 


21 


40 


37 341 


3S589 


61411 


98 753 


20 


41 


37 393 


38 644 


61356 


98 750 


19 


42 


37 445 


38 699 


61301 


9S 746 


18 


43 


37 497 


3S754 


61246 


98 743 


17 


44 


37 549 


38 808 


61192 


98 740 


16 


45 


37 600 


3S863 


61137 


98 737 


15 


46 


37 652 


38 918 


610S2 


98 734 


14 


47 


37 703 


38 972 


61028 


9S731 


B 


48 


37 755 


39 027 


60 973 


98 728 


12 


49 


37 806 


39 0S2 


60 918 


98 725 


11 


50 


37 858 


39 136 


60 864 


98 722 


10 


51 


37 909 


39 190 


60 810 


98 719 


9 


52 


37 960 


39 245 


60 755 


98 715 


8 


53 


38 011 


39 299 


60 701 


98 712 


7 


54 


3S062 


39 353 


60 647 


98 709 


6 


55 


38113 


39 407 


60 593 


98 706 


5 


56 


38 164 


39 461 


60 539 


98 703 


4 


57 


38 215 


39 515 


60 485 


98 700 


3 


58 


38 266 


39 569 


60 431 


98 697 


2 


59 


38 317 


39 623 


60 377 


9S694 


1 


60 


38 368 


39 677 


60 323 


98 690 


O 




9 

log cos 


9 

log cot 


10 

log tan 


9 

log sin 




t 


t 



14 c 



t 


log sin 


log tan 


log cot 


log cos 


/ 




9 

38 368 


9 

39 677 


10 

60 323 


9 

98 690 







60 


1 


38 418 


39 731 


60 269 


98 687 


59 


2 


38 469 


39 785 


60 215 


98 684 


58 


3 


38 519 


39 838 


60162 


98 681 


57 


4 


38 570 


39 892 


60108 


98 678 


56 


5 


38 620 


39 945 


60 055 


98 675 


55 


6 


38 670 


39 999 


60 001 


98 671 


54 


7 


38 721 


40 052 


59 948 


98 668 


53 


8 


38 771 


40106 


59 894 


98 665 


52 


9 


38 821 


40159 


59 841 


98 662 


51 


10 


38 871 


40 212 


59 788 


98 659 


50 


11 


3S921 


40 266 


59 734 


98 656 


49 


12 


38 971 


40 319 


59 681 


98 652 


48 


13 


39 021 


40 372 


59 628 


98 649 


47 


14 


39 071 


40 425 


59 575 


98 646 


46 


15 


39121 


40 478 


59 522 


98 643 


45 


16 


39170 


40 '531 


59 469 


98 640 


44 


17 


39 220 


40 584 


59 416 


98 636 


43 


IS 


39 270 


40 636 


59 364 


98 633 


42 


19 


39 319 


40 689 


59 311 


98 630 


41 


20 


39 369 


40 742 


59 258 


9S627 


40 


21 


39 418 


40 795 


59 205 


98 623 


39 


22 


39 467 


40 847 


59153 


98 620 


3S 


23 


39 517 


40 900 


59100 


98 617 


37 


24 


39 566 


40 952 


59 048 


98 614 


36 


25 


39 615 


41005 


58 995 


98 610 


35 


26 


39 664 


41057 


58 943 


98 607 


34 


27 


39 713 


41109 


58 891 


98 604 


33 


28 


39 762 


41161 


58 839 


98 601 


32 


29 


39 811, 


41214 


58 786 


98 597 


31 


30 


39 860 


41266 


58 734 


98 594 


30 


31 


39 909 


41318 


58 682 


9S591 


29 


32 


39 958 


41370 


58 630 


98 588 


28 


33 


40 006 


41422 


58 578 


98 584 


27 


34 


40 055 


41474 


58 526 


98 581 


26 


35 


40103 


41526 


58 474 


98 578 


25 


36 


40152 


41578 


58 422 


98 574 


24 


37 


40 200 


41629 


58 371 


98 571 


23 


38 


40 249 


41681 


58 319 


98 568 


22 


39 


40 297 


41733 


58 267 


98 565 


21 


40 


40 346 


41784 


58 216 


98 561 


20 


41 


40 394 


41836 


58164 


98 558 


19 


42 


40 442 


41887 


58113 


98 555 


IS 


43 


40 490 


41939 


58 061 


98 551 


17 


44 


40 538 


41990 


58 010 


98 548 


16 


45 


40 586 


42 041 


57 959 


98 545 


15 


46 


40 634 


42 093 


57 907 


98 541 


14 


47 


40 682 


42144 


57 856 


98 538 


13 


48 


40 730 


42195 


57 805 


98 535 


12 


49 


40 77S 


42 246 


57 754 


98 531 


11 


50 


40 825 


42 297 


57 703 


98 528 


10 


51 


40 873 


42 348 


57 652 


98 525 


9 


52 


40 921 


42 399 


57 601 


98 521 


8 


53 


40 968 


42 450 


57 550 


98 518 


7 


54 


41016 


42 501 


57 499 


98 515 


6 


55 


41063 


42 552 


57 448 


98 511 


5 


56 


41111 


42 603 


57 397 


98 508 


4 


57 


41158 


42 653 


57 347 


98 505 


3 


58 


41205 


42 704 


57 296 


98 501 


2 


59 


41252 


42 755 


57 245 


98 49S 


1 


60 


41300 


42 805 


57195 


98 494 







9 

log cos 


9 

log cot 


IO 

log tan 


9 

log sin 




t 


t 



76 ( 



75 c 







15° 






r 


log sin 


log tan 


log cot 


log cos 


r 




9 

41300 


9 

42 805 


io 

57195 


9 

9S494 







60 


1 


41347 


42 856 


57 144 


9S491 


59 


2 


41394 


42 906 


57 094 


98 488 


5S 


3 


41441 


42 957 


57 043 


98 484 


57 


4 


41488 


43 007 


56 993 


98 481 


56 


5 


41535 


43 057 


56 943 


98 477 


55 


6 


41 582 


43 108 


56S92 


9S474 


54 


7 


41628 


43158 


56S42 


9S471 


53 


8~ 


41675 


43 208 


56 792 


98 467 


52 


9 


41722 


43 258 


56 742 


9S464 


51 


10 


41768 


43 30S 


56 692 


9S460 


50 


11 


41815 


43 358 


56 642 


9S457 


49 


12 


41861 


43 40S 


56 592 


98 453 


48 


13 


41908 


43 458 


56 542 


98 450 


47 


14 


41954 


43 508 


56 492 


98 447 


46 


15 


42 001 


43 558 


56 442 


98 443 


45 


16 


42 047 


43 607 


56 393 


9S440 


44 


17 


42 093 


43 657 


56 343 


9S436 


43 


18 


42 140 


43 707 


56 293 


98 433 


42 


19 


42 186 


43 756 


56 244 


98 429 


41 


20 


42 232 


43 806 


56194 


98 426 


40 


21 


42 278 


43 855 


56145 


98 422 


39 


22 


42 324 


43 905 


56 095 


98 419 


38 


23 


42 370 


43 954 


56 046 


98 415 


37 


24 


42 416 


44 004 


55 996 


98 412 


36 


25 


42 461 


44 053 


55 947 


9S409 


35 


26 


42 507 


44102 


55 898 


9S405 


34 


27 


42 553 


44151 


55 849 


98 402 


33 


■28 


42 599 


44 201 


55 799 


98 398 


31 


29 


42 644 


44 250 


55 750 


98 395 


31 


30 


42 690 


44 299 


55 701 


98 391 


30 


31 


42 735 


44 348 


55 652 


9S388 


29 


32 


42 781 


44 397 


55 603 


9S3S4 


28 


33 


42S26 


44 446 


55 554 


9S381 


27 


34 


42 872 


44 495 


55 505 


9S377 


26 


35 


42 917 


44 544 


55 456 


9S373 


25 


36 


42 962 


44 592 


55 40S 


9S370 


24 


37 


43 00S 


44 641 


55 359 


98 366 


23 


38 


43 053 


44 690 


55 310 


98 363 


22 


39 


43 09S 


44 73S 


55 262 


98 359 


21 


40 


43 143 


44 787 


55 213 


98 356 


20 


41 


43 188 


44 836 


55 164 


98 352 


19 


42 


43 233 


44 884 


55 116 


9S349 


18 


43 


43 27S 


44 933 


55 067 


9S345 


17 


44 


43 323 


44 981 


55 019 


98 342 


16 


45 


43 367 


45 029 


54 971 


98 338 


15 


46 


43 412 


45 078 


54 922 


98 334 


14 


47 


43 457 


45 126 


54 874 


98 331 


13 


4S 


43 502 


45 174 


54 826 


98 327 


12 


49 


43 546 


45 222 


54 778 


98 324 


11 


50 


43 591 


45 271 


54 729 


98 320 


10 


51 


43 635 


45 319 


54 681 


98 317 


9 


52 


43 680 


45 367 


54 633 


9S313 


8 


53 


43 724 


45 415 


54 585 


98 309 


7 


54 


43 769 


45 463 


54 537 


9S306 


6 


55 


43 813 


45 511 


54 489 


98 302 


5 


56 


43 857 


45 559 


54 441 


98 299 


4 


57 


43 901 


45 606 


54 394 


9S295 


3 


58 


43 946 


45 654 


54 346 


98 291 


2 


59 


43 990 


45 702 


54 298 


98 28S 


1 


60 


44 034 


45 750 


54 250 


9S284 







9 

log cos 


9 

log cot 


IO 

log tan 


9 

log sin 




t 


r 







16° 




35 


r 


log sin 


log tan 


log cot 


log cos 


t 




9 

44 034 


9 

45 750 


IO 

54 250 


9 

98 284 







60 


1 


44 078 


45 797 


54 203 


98 281 


59 


2 


44 122 


45 845 


54155 


98 277 


58 


3 


44166 


45 892 


54 108 


98 273 


57 


4 


44 210 


45 940 


54 060 


98 270 


56 


5 


44 253 


45 987 


54 013 


98 266 


55 


6 


44 297 


46 035 


53 965 


98 262 


54 


7 


44 341 


46 082 


53 918 


98 259 


53 


S 


44 385 


46130 


53 870 


98 255 


52 


9 


44 428 


46177 


53 823 


98 251 


51 


10 


44 472 


46 224 


53 776 


98 248 


50 


11 


44 516 


46 271 


53 729 


98 244 


49 


12 


44 559 


46 319 


53 681 


98 240 


48 


13 


44 602 


46 366 


53 634 


98 237 


47 


14 


44 646 


46 413 


53 587 


98 233 


46 


15 


44 689 


46 460 


53 540 


98 229 


45 


16 


44 733 


46 507 


53 493 


98 226 


44 


17 


44 776 


46 554 


53 446 


98 222 


43 


18 


44 819 


46 601 


53 399 


98 218 


42 


19 


44 862 


46 648 


53 352 


98 215 


41 


20 


44 905 


46 694 


53 306 


98 211 


40 


21 


44 948 


46 741 


53 259 


98 207 


39 


22 


44 992 


46 788 


53 212 


98 204 


38 


23 


45 035 


46 835 


53 165 


98 200 


37 


24 


45 077 


46 881 


53 119 


98196 


36 


25 


45 120 


46 928 


53 072 


98192 


35 


26 


45 163 


46 975 


53 025 


98189 


34 


27 


45 206 


47 021 


52 979 


98185 


33 


2S 


45 249 


47 068 


52 932 


98 181 


32 


29 


45 292 


47114 


52 886 


98177 


31 


30 


45 334 


47160 


52 840 


9S174 


30 


31 


45 377 


47 207 


52 793 


98 170 


29 


32 


45 419 


47 253 


52 747 


98166 


28 


33 


45 462 


47 299 


52 701 


9S162 


27 


34 


45 504 


47 346 


52 654 


98159 


26 


35 


45 547 


47 392 


52 608 


98155 


25 


36 


45 589 


47 438 


52 562 


98151 


24 


37 


45 632 


47 484 


52 516 


98 147 


23 


38 


45 674 


47 530 


52 470 


98144 


22 


39 


45 716 


47 576 


52 424 


98140 


21 . 


40 


45 758 


47 622 


52 378 


98136 


20 


41 


45 801 


47 668 


52 332 


98132 


19 


42 


45 843 


47 714 


52 286 


9S129 


18 


43 


45 885 


47 760 


52 240 


98125 


17 


44 


45 927 


47 806 


52194 


98121 


16 


45 


45 969 


47 852 


52 148 


98117 


15 


46 


46 011 


47 897 


52 103 


98113 


14 


47 


46 053 


47 943 


52 057 


98 110 


13 


48 


46 095 


47 989 


52 011 


98106 


12 


49 


46136 


48 035 


51965 


98102 


11 


50 


46178 


48 080 


51920 


98 098 


IO 


51 


46 220 


48126 


51874 


98 094 


9 


52 


46 262 


48 171 


51829 


98 090 


8 


53 


46 303 


48 217 


51783 


98 087 


7 


54 


46 345 


48 262 


51738 


9S0S3 


6 


55 


46 386 


48 307 


51693 


98 079 


5 


56 


46 428 


48 353 


51647 


98 075 


4 


57 


46 469 


48 398 


51602 


98 071 


3 


58 


46 511 


48 443 


51 557 


98 067 


2 


59 


46 552 


48 489 


51511 


98 063 


1 


60 


46 594 


48 534 


51466 


98 060 


O 




9 


9 


10 


9 





t 


log cos 


log cot 


log tan 


log sin 


t 



74 c 



73 c 



36 




17° 






t 


log sin 


log tan 


log cot 


log cos 


f 




9 


9 


io 


9 




o 


46 594 


48 534 


51466 


98 060 


00 


1 


46 635 


48 579 


51421 


98 056 


59 


2 


46 676 


48 624 


51376 


98 052 


58 


3 


46 717 


48 669 


51331 


98 048 


57 


4 


46 758 


48 714 


51286 


98 044 


56 


5 


46 800 


48 759 


51241 


98 040 


55 


6 


46 841 


48 804 


51196 


98 036 


54 


7 


46 882 


48 849 


51151 


98 032 


53 


8 


46 923 


48 894 


51 106 


98 029 


52 


9 


46 964 


48 939 


51061 


98 025 


51 


10 


47 005 


48 984 


51016 


98 021 


50 


11 


47 045 


49 029 


50 971 


98 017 


49 


12 


47 086 


49 073 


50 927 


98 013 


48 


13 


47127 


49118 


50 882 


98 009 


47 


14 


47168 


49163 


50 837 


98 005 


46 


15 


47 209 


49 207 


50 793 


98 001 


45 


16 


47 249 


49 252 


50 748 


97 997 


44 


17 


47 290 


49 296 


50 704 


97 993 


43 


18 


47 330 


49 341 


50 659 


97 989 


42 


19 


47 371 


49 385 


50 615 


97 986 


41 


20 


47 411 


49 430 


50 570 


97 982 


40 


21 


47 452 


49 474 


50 526 


97 978 


39 


22 


47 492 


49 519 


50 481 


97 974 


38 


23 


47 533 


49 563 


50 437 


97 970 


37 


24 


47 573 


49 607 


50 393 


97 966 


36 


25 


47 613 


49 652 


50 348 


97 962 


35 


26 


47 654 


49 696 


50 304 


97 958 


34 


27 


47 694 


49 740 


50 260 


97 954 


33 


28 


47 734 


49 784 


50 216 


97 950 


32 


29 


47 774 


49 828 


50172 


97 946 


31 


30 


47 814 


49 872 


50128 


97 942 


30 


31 


47 854 


49 916 


50 084 


97 938 


29 


32 


47 894 


49 960 


50 040 


97 934 


28 


33 


47 934 


50 004 


49 996 


97 930 


27 


34 


47 974 


50 048 


49 952 


97 926 


26 


35 


48 014 


50 092 


49 908 


97 922 


25 


36 


48 054 


50136 


49 864 


97 918 


24 


37 


48 094 


50180 


49 820 


97 914 


23 


38 


48133 


50 223 


49 777 


97 910 


22 


39 


48173 


50 267 


49 733 


97 906 


21 


40 


48 213 


50311 


49 689 


97 902 


20 


41 


48 252 


50 355 


49 645 


97 898 


19 


42 


48 292 


50 398 


49 602 


97 894 


18 


43 


48 332 


50 442 


49 558 


97 890 


17 


44 


48 371 


50 485 


49 515 


97 886 


16 


45 


48 411 


50 529 


49 471 


97 882 


15 


46 


48 450 


50 572 


49 428 


97 878 


14 


47 


48 490 


50 616 


49 384 


97 874 • 


13 


48 


48 529 


50 659 


49 341 


97 870 


12 


49 


48 568 


50 703 


49 297 


97 866 


11 


50 


48 607 


50 746 


49 254 


97S61 


10 


51 


48 647 


50 789 


49 211 


97 857 


9 


52 


48 686 


50 833 


49167 


97 853 


8 


53 


48 725 


50 876 


49 124 


97 849 


7 


54 


48 764 


50 919 


49 081 


97 845 


6 


55 


48 803 


50 962 


49 038 


97 841 


5 


56 


48 842 


51005 


48 995 


97S37 


4 


57 


48 881 


51048 


48 952 


97 833 


3 


58 


48 920 


51092 


48 908 


97 829 


2 


59 


48 959 


51135 


4S865 


97S25 


1 


60 


48 998 


51178 


4S822 


97 821 







9 


9 


IO 


9 





t 


log COS 


log cot 


log tan 


log sin 


t 



18 c 



r 


log sin 


log tan 


log cot 


log cos 


/ 




9 


9 


IO 


9 




O 


48 998 


51 178 


48 822 


97 821 


60 


1 


49 037 


51 221 


48 779 


97 817 


59 


2 


49 076 


51264 


48 736 


97S12 


58 


3 


49115 


51306 


48 694 


97 808 


57 


4 


49153 


51349 


48 651 


97 804 


56 


5 


49 192 


51 392 


48 60S 


97 800 


55 


6 


49 231 


51435 


4S565 


97 796 


54 


7 


49 269 


51478 


48 522 


97 792 


53 


8 


49 308 


51 520 


48 480 


97 78S 


52 


9 


49 347 


51563 


48 437 


97 784 


51 


IO 


49 385 


51606 


48 394 


97 779 


50 


11 


49 424 


51648 


48 352 


97 775 


49 


12 


49 462 


51 691 


48 309 


97 771 


48 


13 


49 500 


51734 


48 266 


97 767 


47 


14 


49 539 


51776 


48 224 


97 763 


46 


15 


49 577 


51819 


48181 


97 759 


45 


16 


49 615 


'51861 


48139 


97 754 


44 


17 


49 654 


51903 


48 097 


97 750 


43 


18 


49 692 


51 946 


48 054 


97 746 


42 


19 


49 730 


51988 


48 012 


97 742 


41 


20 


49 768 


52 031 


47 969 


97 738 


40 


21 


49 806 


52 073 


47 927 


97 734 


39 


22 


49 844 


52 115 


47 885 


97 729 


38 


23 


49 882 


52 157 


47 843 


97 725 


37 


24 


49 920 


52 200 


47 800 


97 721 


36 


25 


49 958 


52 242 


47 758 


97 717 


35 


26 


49 996 


52 284 


47 716 


97 713 


34 


27 


50 034 


52 326 


47 674 


97 708 


33 


28 


50 072 


52 368 


47 632 


97 704 


32 


29 


50410 


52 410 


47 590 


97 700 


31 


30 


50148 


52.452 


47 548 


97 696 


30 


31 


50 185 


52 494 


47 506 


97 691 


29 


32 


50 223 


52 536 


47 464 


97 687 


28 


33 


50 261 


52 578 


47 422 


97 683 


27 


34 


50 298 


52 620 


47 380 


97 679 


26 


35 


50 336 


52 661 


47 339 


97 674 


25 


36 


50 374 


52 703 


47 297 


97 670 


24 


37 


50 411 


52 745 


47 255 


97 666 


23 


38 


50 449 


52 787 


47 213 


97 662 


22 


39 


50 486 


52 829 


47171 


97 657 


21 


40 


50 523 


52 870 


47 130 


97 653 


20 


41 


50 561 


52 912 


47 088 


97 649 


19 


42 


50 598 


52 953 


47 047 


97 645 


18 


43 


50 635 


52 995 


47 005 


97 640 


17 


44 


50 673 


53 037 


46 963 


97 636 


16 


45 


50 710 


53 078 


46 922 


97 632 


15 


46 


50 747 


53 120 


46 880 


97 628 


14 


47 


50 784 


53 161 


46S39 


97 623 


13 


48 


50 821 


53 202 


46 798 


97 619 


12 


49 


50 858 


53 244 


46 756 


97 615 


11 


50 


50 896 


53 285 


46 715 


97 610 


10 


51 


50 933 


53 327 


46 673 


97 606 


9 


52 


50 970 


53 368 


46 632 


97 602 


8 


53 


51007 


53 409 


46 591 


97 597 


7 


54 


51043 


53 450 


46 550 


97 593 


6 


55 


51 0S0 


53 492 


46 508 


97 589 


5 


56 


51117 


53 533 


46 467 


97 584 


4 


57 


51154 


53 574 


46 426 


97 580 


3 


58 


51 191 


53 615 


46 385 


97 576 


2 


59 


51227 


53 656 


46 344 


97 571 


1 


60 


51264 


53 697 


46 303 


97 567 







9 


9 


IO 


9 




t 


log cos 


log cot 


log tan 


log sin 


r 



72 c 



n 







19° 






t 


log sin 


log tan 


log cot 


log cos 


t 




9 

51264 


9 

53 697 


IO 

46 303 


9 

97 567 




o 


60 


1 


51301 


53 73S 


46 262 


97 563 


59 


2 


5133S 


53 779 


46 221 


97 558 


58 


3 


51374 


53 820 


46 180 


97 554 


57 


4 


51411 


53 861 


46139 


97 550 


56 


5 


51447 


53 902 


46 098 


97 545 


55 


6 


514S4 


53 943 


46 057 


97 541 


54 


7 


51520 


53 984 


46 016 


97 536 


53 


8' 


51 557 


54 025 


45 975 


97 532 


52 


9 


51593 


54 065 


45 935 


97 528 


51 


io 


51629 


54106 


45 894 


97 523 


50 


11 


51666 


54147 


45 853 


97 519 


49 


12 


51702 


541S7 


45 813 


97 515 


48 


13 


51738 


S4 22S 


45 772 


97 510 


47 


14 


51774 


54 269 


45 731 


97 506 


46 


15 


51811 


54 309 


45 691 


97 501 


45 


16 


51847 


54 350 


45 650 


97 497 


44 


17 


518S3 


54 390 


45 610 


97 492 


43 


18 


51919 


54 431 


45 569 


97 488 


42 


19 


51955 


54 471 


45 529 


97 484 


41 


20 


51991 


54 512 


45 488 


97 479 


40 


21 


52 027 


54 552 


45 448 


97 475 


39 


22 


52 063 


54 593 


45 407 


97 470 


38 


23 


52 099 


54 633 


45 367 


97*466 


37 


24 


52 135 


54 673 


45 327 


97 461 


36 


25 


52171 


54 714 


45 286 


97 457 


35 


26 


52 207 


54 754 


45 246 


97 453 


34 


27 


52 242 


54 794 


45 206 


97 448 


33 


28 


52 27S 


54 835 


45 165 


97 444 


32 


29 


52 314 


54 875 


45 125 


97 439 


31 


30 


52 350 


54 915 


45 0S5 


97 435 


30 


31 


52 385 


54 955 


45 045 


97 430 


29 


32 


52 421 


54 995 


45 005 


97 426 


28 


33 


52 456 


55 035 


44 965 


97 421 


27 


34 


52 492 


55 075 


44 925 


97 417 


26 


35 


52 527 


55115 


44 885 


97 412 


25 


36 


52 563 


55 155 


44 845 


97 408 


24 


37 


52 598 


55 195 


44 805 


97 403 


23 


3S 


52 634 


55 235 


44 765 


97 399 


22 


39 


52 669 


55 275 


44 725 


97 394 


21 


40 


52 705 


55 315 


44 685 


97 390 


20 


41 


52 740 


55 355 


44 645 


97 385 


19 


42 


52 775 


55 395 


44 605 


97 3S1 


18 


43 


52 811 


55 434 


44 566 


97 376 


17 


44 


52 846 


55 474 


44 526 


97 372 


16 


45 


52 881 


55 514 


44 486 


97 367 


15 


46 


52 916 


55 554 


44 446 


97 363 


14 


47 


52 951 


55 593 


44 407 


97 358 


13 


48 


52 986 


55 633 


44 367 


97 353 


12 


49 


53 021 


55 673 


44 327 


97 349 


11 


SO 


53 056 


55 712 


44 2SS 


97 344 


IO 


51 


53 092 


55 752 


44 248 


97 340 


9 


52 


53 126 


55 791 


44 209 


97 335 


8 


53 


53 161 


55 831 


44 169 


97 331 


7 


54 


53 196 


55 870 


44130 


97 326 


6 


55 


53 231 


55 910 


44 090 


97 322 


5 


56 


53 266 


55 949 


44 051 


97 317 


4 


57 


53 301 


55 989 


44 011 


97 312 


3 


58 


53 336 


56 028 


43 972 


97 308 


2 


59 


53 370 


56 067 


43 933 


97 303 


1 


60 


53 405 


56 107 


43 893 


97 299 


O 




9 

log cos 


9 

log cot 


10 

log tan 


9 

log sin 




f 


t 







20° 




37 


t 


log sin 


log tan 


log cot 


log cos 


t 




9 


9 


IO 


9 







53 405 


56107 


43 893 


97 299 


60 


1 


53 440 


56146 


43 854 


97 294 


59 


2 


53 475 


561S5 


43 815 


97 289 


58 


3 


53 509 


56 224 


43 776 


97 285 


57 


4 


53 544 


56 264 


43 736 


97 280 


56 


5 


53 578 


56 303 


43 697 


97 276 


55 


6 


53 613 


56 342 


43 65S 


97 271 


54 


7 


53 647 


56 381 


43 619 


97 266 


53 


8 


53 682 


56 420 


43 580 


97 262 


52 


9 


53 716 


56 459 


43 541 


97 257 


51 


10 


53 751 


56 498 


43 502 


97 252 


50 


11 


53 785 


56 537 


43 463 


97 248 


49 


12 


53 819 


56 576 


43 424 


97 243 


48 


13 


53 854 


56 615 


43 385 


97 238 


47 


14 


53 88S 


56 654 


43 346 


97 234 


46 


15 


53 922 


56 693 


43 307 


97 229 


45 


16 


53 957 


56 732 


43 268 


97 224 


44 


17 


53 991 


56 771 


43 229 


97 220 


43 


18 


54 025 


56 810 


43 190 


97 215 


42 


19 


54 059 


56 849 


43 151 


97 210 


41 


20 


54 093 


56 887 


43 113 


97 206 


40 


21 


54 127 


56 926 


43 074 


97 201 


39 


22 


54161 


56 965 


43 035 


97 196 


38 


23 


54195 


57 004 


42 996 


97 192 


37 


24 


54 229 


57 042 


42 958 


97187 


36 


25 


54 263 


57 081 


42 919 


97 182 


35 


26 


54 297 


57120 


42 880 


97 178 


34 


27 


54 331 


57158 


42 842 


97 173 


33 


28 


54 365 


57 197 


42 S03 


97 168 


32 


29 


54 399 


57 235 


42 765 


97163 


31 


30 


54 433 


57 274 


42 726 


97159 


30 


31 


54 466 


57 312 


42 688 


97 154 


29 


32 


54 500 


57 351 


42 649 


97 149 


28 


33 


54 534 


57 389 


42 611 


97 145 


27 


34 


54 567 


57 428 


42 572 


97 140 


26 


35 


54 601 


57 466 


42 534 


97135 


25 


36 


54 635 


57 504 


42 496 


97 130 


24 


37 


54 668 


57 543 


42 457 


97 126 


23 


38 


54 702 


57 581 


42 419 


97 121 


22 


39 


54 735 


57 619 


42 381 


97116 


21 


40 


54 769 


57 658 


42 342 


97 111 


20 


41 


54 802 


57 696 


42 304 


97 107 


19 


42 


54 836 


57 734 


42 266 


97 102 


IS 


43 


54 869 


57 772 


42 228 


97 097 


17 


44 


54 903 


57 810 


42 190 


97 092 


16 


45 


54 936 


57 849 


42 151 


97 087 


15 


46 


54 969 


57 887 


42 113 


97 083 


14 


47 


55 003 


57 925 


42 075 


97 078 


13 


48 


55 036 


57 963 


42 037 


97 073 


12 


49 


55 069 


58 001 


41999 


97 068 


11 


50 


55 102 


58 039 


41961 


97 063 


10 


51 


55 136 


58 077 


41923 


97 059 


9 


52 


55 169 


58 115 


41 885 


97 054 


8 


53 


55 202 


58153 


41847 


97 049 


7 


54 


55 235 


58 191 


41809 


97 044 


6 


55 


55 268 


58 229 


41771 


97 039 


5 


56 


55 301 


58 267 


41733 


97 035 


4 


57 


55 334 


58 304 


41 696 


97 030 


3 


58 


55 367 


5S 342 


41 658 


97 025 


2 


59 


55 400 


58 380 


41620 


97 020 


1 


60 


55 433 


58 418 


41582 


97 015 


O 




9 

log cos 


9 

log cot 


IO 

log tan 


9 

log sin 




t 


t 



w 



69 c 



38 




21° 






t 


log sin 


log tan 


log cot 


log cos 


t 




9 

55 433 


9 

58 418 


IO 

41582 


9 

97 015 




o 


60 


1 


55 466 


58 455 


41545 


97 010 


59 


2 


55 499 


58 493 


41507 


97 005 


58 


3 


55 532 


58 531 


41469 


97 001 


57 


4. 


55 564 


58 569 


41431 


96 996 


56 


5 


55 597 


58 606 


41394 


96 991 


55 


6 


55 630 


58 644 


41356 


96 986 


54 


7 


55 663 


58 681 


41319 


96 981 


53 


8 


55 695 


58 719 


41281 


96 976 


52 


9 


55 72S 


58 757 


41243 


96 971 


51 


io 


55 761 


58 794 


41206 


96 966 


50 


11 


55 793 


58 832 


41168 


96 962 


49 


12 


55 826 


58 869 


41131 


96 957 


48 


13 


55 858 


58 907 


41093 


96 952 


47 


14 


55 891 


58 944 


41056 


96 947 


46 


15 


55 923 


58 981 


41019 


96 942 


45 


16 


55 956 


59 019 


40 981 


96 937 


44 


17 


55 988 


59 056 


40 944 


96 932 


43 


18 


56 021 


59 094 


40 906 


96 927 


42 


19 


56 053 


59131 


40 869 


96 922 


41 


20 


56 085 


59168 


40 832 


96 917 


40 


21 


56118 


59 205 


40 795 


96 912 


39 


22 


56150 


59 243 


40 757 


96 907 


38 


23 


56182 


59 280 


40 720 


96 903 


37 


24 


56 215 


59 317 


40 683 


96 898 


36 


25 


56 247 


59 354 


40 646 


96 893 


35 


26 


56 279 


59 391 


40 609 


96 888 


34 


27 


56 311 


59 429 


40 571 


96 883 


33 


28 


56 343 


59 466 


40 534 


96 878 


32 


29 


56 375 


59 503 


40 497 


96 873 


31 


30 


56 408 


59 540 


40 460 


96 868 


30 


31 


56 440 


59 577 


40 423 


96 863 


29 


32 


56 472 


59 614 


40 386 


96 858 


28 


33 


56 504 


59 651 


40 349 


96 853 


27 


34 


56 536 


59 688 


40 312 


96 848 


26 


35 


56 568 


59 725 


40 275 


96 843 


25 


36 


56 599 


59 762 


40 238 


96 838 


24 


37 


56 631 


59 799 


40 201 


96 833 


23 


38 


56 663 


59 835 


40165 


96 828 


22 


39 


56 695 


59 872 


40128 


96 823 


21 


40 


56 727 


59 909 


40 091 


96 818 


20 


41 


56 759 


59 946 


40 054 


96 813 


19 


42 


56 790 


59 983 


40 017 


96 808 


18 


43 


56 822 


60 019 


39 981 


96 803 


17 


44 


56 854 


60 056 


39 944 


96 798 


16 


45 


56 886 


60 093 


39 907 


96 793 


15 


46 


56 917 


60130 


39 870 


96 788 


14 


47 


56 949 


60166 


39S34 


96 783 


13 


48 


56 980 


60 203 


39 797 


96 778 


12 


49 


57 012 


60 240 


39 760 


96 772 


11 


50 


57 044 


60 276 


39 724 


96 767 


IO 


51 


57 075 


60 313 


39 687 


96 762 


9 


52 


57107 


60 349 


39 651 


96 757 


8 


53 


57 138 


60 386 


39 614 


96 752 


7 


54 


57169 


60 422 


39 578 


96 747 


6": 


55 


57 201 


60 459 


39 541 


96 742 


5 


56 


57 232 


60 495 


39 505 


96 737 


4 


57 


57 264 


60 532 


39 468 


96 732 


3 


58 


57 295 


60 568 


39 432 


96 727 


2 


59 


57 326 


60 605 


39 395 


96 722 


1 


60 


57 358 


60 641 


39 359 


96 717 







9 

log COS 


9 

log cot 


IO 

log tan 


9 

log sin 




t 


f 



22 c 



t 


log sin 


log tan 


log cot 


log cos 


/ 




9 


9 


10 


9 






o 


57 358 


60 641 


39 359 


96 717 


60 


1 


57 389 


60 677 


39 323 


96 711 


59 


2 


57 420 


60 714 


39 286 


96 706 


58 


3 


57 451 


60 750 


39 250 


96 701 


57 


4 


57 482 


60 786 


39 214 


96 696 


56 


5 


57 514 


60 823 


39177 


96 691 


55 


6 


57 545 


60 859 


39141 


96 686 


54 


7 


57 576 


60 895 


39105 


96 681 


53 


8 


57 607 


60 931 


39 069 


96 676 


52 


9 


57 638 


60 967 


39 033 


96 670 


51 


10 


SI 669 


61004 


38 996 


96 665 


50 


11 


57 700 


61040 


38 960 


96 660 


49 


12 


57 731 


61076 


38 924 


96 655 


48 


13 


57 762 


61112 


38 888 


96 650 


47 


14 


57 793 


61148 


38 852 


96 645 


46 


15 


57 824 


61184 


38 816 


96 640 


45 


16 


57 855 


61220 


38 780 


96 634 


44 


17 


57 885 


61256 


38 744 


96 629 


43 


18 


57 916 


61292 


38 708 


96 624 


42 


19 


57 947 


61328 


38 672 


96 619 


41 


20 


57 978 


61364 


38 636 


96 614 


40 


21 


58 008 


61400 


38 600 


96 608 


39 


22 


58 039 


61436 


38 564 


96 603 


38 


23 


58 070 


61472 


38 528 


96 598 


37 


24 


58101 


61508 


38 492 


96 593 


36 


25 


58131 


61544 


38 456 


96 588 


35 


26 


58 162 


61579 


38 421 


96 582 


34 


27 


58192 


61615 


38 385 


96 577 


33 


28 


58 223 


61651 


38 349 


96 572 


32 


29 


58 25^3 


61687 


38 313 


96 567 


31 


30 


58 284 


61722 


38 278 


96 562 


30 


31 


58 314 


61758 


38 242 


96 556 


29 


32 


58 345 


61794 


38 206 


96 551 


28 


33 


58 375 


61830 


38170 


96 546 


27 


34 


58 406 


61865 


38135 


96 541 


26 


35 


58 436 


61901 


38 099 


96 535 


25 


36 


58 467 


61936 


38 064 


96 530 


24 


37 


58 497 


61972 


38 028 


96 525 


23 


38 


58 527 


62 008 


37 992 


96 520 


22 


39 


58 557 


62 043 


37 957 


96 514 


21 


40 


58 588 


62 079 


37 921 


96 509 


20 


41 


58 618 


62 114 


37 886 


96 504 


19 


42 


58 648 


62150 


37 850 


96 498 


18 


43 


58 678 


62 185 


37 815 


96 493 


17 


44 


58 709 


62 221 


37 779 


96 488 


16 


45 


58 739 


62 256 


37 744 


96 483 


15 


46 


58 769 


62 292 


37 708 


96 477 


14 


47 


58 799 


62 327 


37 673 


96 472 


13 


48 


58 829 


62 362 


37 638 


96 467 


12 


49 


58 859 


62 398 


37 602 


96 461 


11 


50 


58 889 


62 433 


37 567 


96 456 


IO 


51 


58 919 


62 468 


37 532 


96 451 


9 


52 


58 949 


62 504 


37 496 


96 445 


8 


53 


58 979 


62 539 


37 461 


96 440 


7 


54 


59 009 


62 574 


37 426 


96 435 


6 


55 


59 039 


62 609 


37 391 


96 429 


5 


56 


59 069 


62 645 


37 355 


96 424 


4 


57 


59 098 


62 680 


37 320 


96 419 


3 


58 


59128 


62 715 


37 285 


96 413 


2 


59 


59158 


62 750 


37 250 


96 408 


1 


60 


5918S 


62 785 


37 215 


96 403 







9 


9 


IO 


9 




r 


log cos 


log cot 


log tan 


log sin 


t 



68' 



67 c 



23 ( 



t 


log sin log tan 


log cot 


log cos 


r 




9 9 


10 


9 




o 


5918S 62 785 


37 215 


96 403 


60 


1 


59 218 62 820 


37 180 


96 397 


59 


2 


59 247 62 855 


37 145 


96 392 


58 


3 


59 277 62 890 


37110 


96 387 


57 


4 


59 307 62 926 


37 074 


96 381 


56 


5 


59 336 62 961 


37 039 


96 376 


55 


6 


59 366 62 996 


37 004 


96 370 


54 


7 


59 396 63 031 


36 969 


96 365 


53 


8 


'59 425 63 066 


36 934 


96 360 


52 


9 


59 455 63 101 


36 899 


96 354 


51 


10 


59 484 63 135 


36 865 


96 349 


50 


11 


59 514 63 170 


36 830 


96 343 


49 


12 


59 543 63 205 


36 795 


96 338 


48 


13 


59 573 63 240 


36 760 


96 333 


47 


14 


59 602 63 275 


36 725 


96 327 


46 


15 


59 632 63 310 


36 690 


96 322 


45 


16 


59 661 63 345 


36 655 


96 316 


44 


17 


59 690 63 379 


36 621 


96 311 


43 


18 


59 720 63 414 


36 586 


96 305 


42 


19 


59 749 _ 63 449 


36 551 


96 300 


41 


20 


59 778 63 484 


36 516 


96 294 


40 


21 


59 808 63 519 


36 481 


96 289 


39 


22 


59 837 63 553 


36 447 


96 284 


38 


23 


59 866 63 58S 


36 412 


96 278 


37 


24 


59 895 63 623 


36 377 


96 273 


36 


25 


59 924 63 657 


36 343 


96 267 


35 


26 


59 954 63 692 


36 308 


96 262 


34 


27 


59 983 63 726 


36 274 


96 256 


33 


28 


60 012 63 761 


36 239 


96 251 


32 


29 


60 041 63 796 


36 204 


96 245 


31 


30 


60 070 63 830 


36 170 


96 240 


30 


31 


60 099 63 865 


36 135 


96 234 


29 


32 


60128 63 899 


36101 


96 229 


2S 


33 


60157 63 934 


36 066 


96 223 


27 


34 


60186 63 968 


36 032 


96 218 


26 


35 


60 215 64 003 


35 997 


96 212 


25 


36 


60 244 64 037 


35 963 


96 207 


24 


37 


60 273 64 072 


35 928 


96 201 


23 


38 


60 302 64106 


35 894 


96196 


22 


39 


60 331 64140 


35 860 


96190 


21 


40 


60 359 64175 


35 825 


96 185 


20 


41 


60 388 64 209 


35 791 


96179 


19 


42 


60 417 64 243 


35 757 


96174 


18 


43 


60 446 64 278 


35 722 


96168 


17 


44 


60 474 64 312 


35 688 


96162 


16 


45 


60 503 64 346 


35 654 


96157 


15 


46 


60 532 64 381 


35 619 


96151 


14 


47 


60 561 64 415 


35 585 


96146 


13 


48 


60 589 64 449 


35 551 


96140 


12 


49 


60 618 64 483 


35 517 


96135 


11 


50 


•60 646 64 517 


35 483 


96129 


io 


51 


60 675 64 552 


35 448 


96123 


9 


52 


60 704 64 586 


35 414 


96118 


8 


53 


60 732 64 620 


35 380 


96112 


7 


54 


60 761 64 654 


35 346 


96107 


6 


55 


60 789 64 688 


35 312 


96101 


5 


56 


60 818 64 722 


35 278 


96 095 


4 


57 


60 846 64 756 


35 244 


96 090 


3 


58 


60 875 64 790 


35 210 


96 084 


2 


59 


60 903 64 824 


35 176 


96 079 


1 


60 


60 931 64 858 


35 142 


96 073 


O 




9 9 

log cos log cot 


10 

log tan 


9 

log sin 




t 


t 







24° 




39 


t 


log sin 


log tan 


log cot 


log cos 


t 






60 931 


9 

64 858 


IO 

35 142 


9 

96 073 







60 


1 


60 960 


64 892 


35 108 


96 067 


59 


2 


60 988 


64 926 


35 074 


96 062 


58 


3 


61016 


64 960 


35 040 


96 056 


57 


4 


61045 


64 994 


35 006 


96 050 


56 


5 


61073 


65 028 


34 972 


96 045 


55 


6 


61 101 


65 062 


34 938 


96 039 


54 


7 


61129 


65 096 


34 904 


96 034 


53 


8 


61158 


65 130 


34 870 


96 028 


52 


9 


61186 


65 164 


34 836 


96 022 


51 


10 


61214 


65 197 


34 803 


96 017 


50 


11 


61242 


65 231 


34 769 


96 011 


49 


12 


61270 


65 265 


34 735 


96 005 


48 


13 


61298 


65 299 


34 701 


96 000 


47 


14 


61326 


65 333 


34 667 


95 994 


46 


15 


61354 


65 366 


34 634 


95 988 


45 


16 


61382 


65 400 


34 600 


95 982 


44 


17 


61411 


65 434 


34 566 


95 977 


43 


18 


61438 


65 467 


34 533 


95 971 


42 


19 


61466 


65 501 


34 499 


95 965 


41 


20 


61494 


65 535 


34 465 


95 960 


40 


21 


61522 


65 568 


34 432 


95 954 


39 


22 


61550 


65 602 


34 398 


95 948 


38 


23 


61578 


65 636 


34 364 


95 942 


37 


24 


61606 


65 669 


34 331 


95 937 


36 


25 


61634 


65 703 


34 297 


95 931 


35 


26 


61662 


65 736 


34 264 


95 925 


34 


27 


61689 


65 770 


34 230 


95 920 


33 


28 


61717 


65 803 


34197 


95 914 


32 


29 


61745 


65 837 


34163 


95 908 


31 


30 


61773 


65 870 


34130 


95 902 


30 


31 


61800 


65 904 


34 096 


95 897 


29 


32 


61828 


65 937 


34 063 


95 891 


28 


33 


61856 


65 971 


34 029 


95 885 


27 


34 


61883 


66 004 


33 996 


95 879 


26 


35 


61911 


66 038 


33 962 


95 873 


25 


36 


61939 


66 071 


33 929 


95 868 


24 


37 


61966 


66104 


33 896 


95 862 


23 


38 


61994 


66138 


33 862 


95 856 


22 


39 


62 021 


66171 


33 829 


95 850 


21 


40 


62 049 


66 204 


33 796 


95 844 


20 


41 


62 076 


66 238 


33 762 


95 839 


19 


42 


62 104 


66 271 


33 729 


95 833 


18 


43 


62 131 


66 304 


33 696 


95 827 


17 


44 


62 159 


66 337 


33 663 


95 821 


16 


45 


62 186 


66 371 


33 629 


95 815 


15 


46 


62 214 


66 404 


33 596 


95 810 


14 


47 


62 241 


66 437 


33 563 


95 804 


13 


48 


62 268 


66 470 


33 530 


95 798 


12 


49 


62 296 


66 503 


33 497 


95 792 


11 


50 


62 323 


66 537 


33 463 


95 786 


10 


51 


62 350 


66 570 


33 430 


95 780 


9 


52 


62 377 


66 603 


33 397 


95 775 


8 


53 


62 405 


66 636 


33 364 


95 769 


7 


54 


62 432 


66 669 


33 331 


95 763 


6 


55 


62 459 


66 702 


33 298 


95 757 


5 


56 


62 486 


66 735 


33 265 


95 751 


4 


57 


62 513 


66 768 


33 232 


95 745 


3 


58 


62 541 


66 801 


33 199 


95 739 


2 


59 


62 56S 


66 834 


33 166 


95 733 


1 


60 


62 595 


66 867 


33 133 


95 728 







9 

log cos 


9 

log cot 


10 

log tan 


9 

log sin 




r 


t 



66 c 



65 ( 



40 




25° 






t 


log sin 


log tan 


log cot 


log cos 


t 




9 


9 


io 


9 









62 595 


66 867 


33 133 


95 728 


60 


1 


62 622 


66 900 


33 100 


95 722 


59 


2 


62 649 


66 933 


33 067 


95 716 


58 


3 


62 676 


66 966 


33 034 


95 710 


57 


4 


62 703 


66 999 


33 001 


95 704 


56 


5 


62 730 


67 032 


32 968 


95 698 


55 


6 


62 757 


67 065 


32 935 


95 692 


54 


7 


62 784 


67 098 


32902 


95 686 


53 


8 


62 811 


67 131 


32 869 


95 680 


52 


9 


62 838 


67163 


32 837 


95 674 


51 


10 


62 865 


67196 


32 804 


95 668 


50 


11 


62 892 


67 229 


32 771 


95 663 


49 


12 


62 918 


67 262 


32 738 


95 657 


48 


13 


62 945 


67 295 


32 705 


95 651 


47 


14 


62 972 


67 327 


32 673 


95 645 


46 


15 


62 999 


67 360 


32 640 


95 639 


45 


16 


63 026 


67 393 


32 607 


95 633 


44 


17 


63 052 


67 426 


32 574 


95 627 


43 


18 


63 079 


67 458 


32 542 


95 621 


42 


19 


63 106 


67 491 


32 509 


95 615 


41 


20 


63133 


67 524 


32 476 


95 609 


40 


21 


63 159 


67 556 


32 444 


95 603 


39 


22 


63 186 


67 589 


32 411 


95 597 


38 


23 


63 213 


67 622 


32 378 


95 591 


37 


24 


63 239 


67 654 


32 346 


95 585 


36 


25 


63 266 


67 687 


32 313 


95 579 


35 


26 


63 292 


67 719 


32 281 


95 573 


34 


27 


63 319 


67 752 


32 248 


95 567 


33 


28 


63 345 


67 785 


32 215 


95 561 


32 


29 


63 372 


67 817 


32 183 


95 555 


31 


30 


63 398 


67 850 


32150 


95 549 


30 


31 


63 425 


67 882 


32 118 


95 543 


29 


32 


63 451 


67 915 


32 085 


95 537 


28 


33 


63 478 


67 947 


32 053 


95 531 


27 


34 


63 504 


67 980 


32 020 


95 525 


26 


35 


63 531 


68 012 


319S8 


95 519 


25 


36 


63 557 


68 044 


31956 


95 513 


24 


37 


63 583 


6S077 


31923 


95 507 


23 


38 


63 610 


68109 


31891 


95 500 


22 


39 


63 636 


68] 42 


31858 


95 494 


21 


40 


63 662 


68174 


31826 


95 488 


20 


41 


63 689 


68 206 


31794 


95 482 


19 


42 


63 715 


68 239 


31761 


95 476 


18 


43 


63 741 


68 271 


31729 


95 470 


17 


44 


63 767 


68 303 


31697 


95 464 


16 


45 


63 794 


68 336 


31664 


95 458 


15 


46 


63 820 


68 36S 


31632 


95 452 


14 


47 


63 846 


68 400 


31600 


95 446 


13 


48 


63 872 


68 432 


31 568 


95 440 


12 


49 


63 898 


68 465 


31535 


95 434 


11 


50 


63 924 


68 497 


31503 


95 427 


10 


51 


63 950 


68 529 


31471 


95 421 


9 


52 


63 976 


68 561 


31439 


95 415 


8 


53 


64 002 


68 593 


31407 


95 409 


- 7 


54 


64 028 


68 626 


31374 


95 403 


6 


55 


64 054 


68 658 


31342 


95 397 


5 


56 


64 080 


68 690 


31310 


95 391 


4 


57 


64 106 


68 722 


31278 


95 384 


3 


5S 


64132 


68 754 


31246 


95 378 


2 


59 


64 158 


68 786 


31214 


95 372 


1 


60 


64184 


68 818 


31182 


95 366 







9 


9 


IO 


9 




t 


log cos 


log cot 


log tan 


log sin " 


t 



26 c 



t 


log sin 


log tan 


log cot 


log cos 


f 




9 


9 


10 


9 




o 


64184 


68 818 


31182 


95 366 


60 


1 


64 210 


68 850 


31150 


95 360 


59 


2 


64 236 


68 882 


31118 


95 354 


58 


3 


64 262 


68 914 


31086 


95 348 


57 


4 


64 288 


68 946 


31054 


95 341 


56 


5 


64 313 


68 978 


31022 


95 335 


55 


6 


64 339 


69 010 


30 990 


95 329 


54 


7 


64 365 


69 042 


30 958 


95 323 


53 


8 


64 391 


69 074 


30 926 


95 317 


52 


9 


64 417 


69106 


30 894 


95 310 


51 


IO 


64 442 


69138 


30 862 


95 304 


50 


11 


64 46S 


69170 


30 830 


95 298 


49 


12 


64 494 


69 202 


30 798 


95 292 


48 


13 


64 519 


69 234 


30 766 


95 286 


47 


14 


64 545 


69 266 


30 734 


95 279 


46 


15 


64 571. 


69 298 


30 702 


95 273 


45 


16 


64 596 


69 329 


30 671 


95 267 


44 


17 


64 622 


69 361 


30 639 


95 261 


43 


18 


64 647 


69 393 


30 607 


95 254 


42 


19 


64 673 


69 425 


30 575 


95 248 


41 


20 


64 698 


69 457 


30 543 


95 242 


40 


21 


64 724 


69 488 


30 512 


95 236 


39 


22 


64 749 


69 520 


30 480 


95 229 


38 


23 


64 775 


69 552 


30 448 


95 223 


37 


24 


64 800 


69 584 


30 416 


95 217 


36 


25 


64 826 


69 615 


30 385 


95 211 


35 


26 


64 851 


69 647 


30 353 


95 204 


34 


27 


64 877 


69 679 


30 321 


95 198 


33 


28 


64902 


69 710 


30 290 


95 192 


32 


29 


.64 927 


69 742 


30 258 


95 185 


31 


30 


64 953 


69 774 


30 226 


95 179 


30 


31 


64 978 


69 805 


30195 


95 173 


29 


32 


65 003 


69 837 


30163 


95 167 


28 


33 


65 029 


69 868 


30132 


95 160 


27 


34 


65 054 


69 900 


30100 


95 154 


26 


35 


65 079 


69 932 


30 068 


95 148 


25 


36 


65 104 


69 963 


30 037 


95 141 


24 


37 


65 130 


69 995 


30 005 


95 135 


23 


38 


65 155 


70 026 


29 974 


95 129 


22 


39 


65 180 


70 058 


29 942 


95 122 


21 


40 


65 205 


70 089 


29 911 


95 116 


20 


41 


65 230 


70 121 


29 879 


95 110 


19 


42 


65 255 


70152 


29 848 


95 103 


18 


43 


65 281 


70184 


29 816 


95 097 


17 


44 


65 306 


70 215 


29 785 


95 090 


16 


45 


65 331 


70 247 


29 753 


95 084 


15 


46 


65 356 


70 278 


29 722 


95 078 


14 


47 


65 381 


70 309 


29 691 


95 071 


13 


48 


65 406 


70 341 


29 659 


95 065 


12 


49 


65 431 


70 372 


29 628 


95 059 


11 


50 


65 456 


70 404 


29 596 


95 052 


10 


51 


65 481 


70 435 


29 565 


95 046 


9 


52 


65 506 


70 466 


29 534 


95 039 


8 


53 


65 531 


70 498 


29 502 


95 033 


7 


54 


65 556 


70 529 


29 471 


95 027 


6 


55 


65 580 


70 560 


29 440 


95 020 


5 


56 


65 605 


70 592 


29 408 


95 014 


4 


57 


65 630 


70 623 


29 377 


95 007 


3 


58 


65 655 


70 654 


29 346 


95 001 


2 


59 


65 680 


70 6S5 


29 315 


94 995 


1 


60 


65 705 


70 717 


29 283 


94 988 







9 


9 


10 


9 






r 


log cos 


log cot 


log tan 


log sin 


t 



64 c 



63 c 



27' 



t 


log sin 


log tan 


log cot 


log cos 


t 




9 

65 705 


9 

70 717 


10 

29 283 


9 

94 988 




o 


60 


1 


65 729 


70 748 


29 252 


94 982 


59 


2 


65 754 


70 779 


29 221 


94 975 


58 


3 


65 779 


70 810 


29190 


94 969 


57 


4 


65 804 


70 841 


29159 


94 962 


56 


5 


65 828 


70 873 


29127 


94 956 


55 


6 


65 853 


70 904 


29 096 


94 949 


54 


7 


65 878 


70 935 


29 065 


94 943 


53 


S 


65 902 


70 966 


29 034 


94 936 


52 


9 


65 927 


70 997 


29 003 


94 930 


51 


10 


65 952 


71028 


28 972 


94 923 


50 


11 


65 976 


71059 


28 941 


94 917 


49 


12 


66 001 


71090 


28 910 


94 911 


48 


13 


66 025 


71121 


28 879 


94 904 


47 


14 


66 050 


71153 


28 847 


94 898 


46 


15 


66 075 


71184 


28 816 


94 891 


45 


16 


66 099 


71215 


28 785 


94 885 


44 


17 


66124 


71246 


28 754 


94 878 


43 


18 


66148 


71277 


28 723 


94 871 


42 


19 


66173 


71308 


28 692 


94 865 


41 


20 


66197 


71339 


28 661 


94S58 


40 


21 


66 221 


71370 


28 630 


94 852 


39 


22 


66 246 


71401 


28 599 


94 845 


38 


23 


66 270 


71431 


2S569 


94 839 


37 


24 


66 295 


71462 


28 538 


94 832 


36 


25 


66 319 


71493 


28 507 


94 826 


35 


26 


66 343 


71524 


28 476 


94 819 


34 


27 


66 368 


71555 


28 445 


94S13 


33 


28 


66 392 


71586 


28 414 


94 806 


32 


29 


66 416 


71617 


28 383 


94 799 


31 


30 


66 441 


71648 


28 352 


94 793 


30 


31 


66465 


71679 


28 321 


94 786 


29 


32 


66 489 


71709 


28 291 


94 780 


28 


33 


66 513 


71740 


28 260 


94 773 


27 


34 


66 537 


71771 


28 229 


94 767 


26 


35 


66 562 


71802 


28 19S 


94 760 


25 


36 


66586 


71833 


28 167 


94 753 


24 


37 


66 610 


71863 


28137 


94 747 


23 


38 


66 634 


71894 


28106 


94 740 


22 


39 


66 658 


71925 


28 075 


94 734 


21 


40 


66 6S2 


71955 


28 045 


94 727 


20 


41 


66 706 


71986 


28 014 


94 720 


19 


42 


66 731 


72 017 


27 983 


94 714 


18 


43 


66 755 


72 048 


27 952 


94 707 


17 


44 


66 779 


72 078 


27 922 


94 700 


16 


45 


66 803 


72 109 


27 891 


94 694 


15 


46 


66 827 


72 140 


27 860 


94 6S7 


14 


47 


66 851 


72 170 


27 830 


94 680 


13 


48 


66 875 


72 201 


27 799 


94 674 


12 


49 


66 899 


72 231 


27 769 


94 667 


11 


50 


66 922 


72 262 


27 73S 


94 660 


10 


51 


66 946 


72 293 


27 707 


94 654 


9 


52 


66 970 


72 323 


27 677 


94 647 


8 


53 


66 994 


72 354 


27 646 


94 640 


7 


54 


67 018 


72 384 


27 616 


94 634 


6 


55 


67 042 


72 415 


27 585 


94 627 


5 


56 


67 066 


72 445 


27 555 


94 620 


4 


57 


67 090 


72 476 


27 524 


94 614 


3 


58 


67 113 


72 506 


27 494 


94 607 


2 


59 


67137 


72 537 


27 463 


94 600 


1 


60 


67161 


72 567 


27 433 


94 593 


O 




9 


9 


10 


9 




t 


log cos 


log cot 


log tan 


log sin 


r 







28° 




41 


r 


log sin 


log tan 


log cot 


log cos 


r 




9 

67 161 


9 

72 567 


10 

27 433 


9 

94 593 







60 


1 


67185 


72 598 


27 402 


94 587 


59 


2 


67 208 


72 628 


27 372 


94 580 


58 


3 


67 232 


72 659 


27 341 


94 573 


57 


4 


67 256 


72 689 


27 311 


94 567 


56 


5 


67 280 


72 720 


27 280 


94 560 


55 


6 


67 303 


72 750 


27 250 


94 553 


54 


7 


67 327 


72 780 


27 220 


94 546 


53 


8 


67 350 


72 811 


27 189 


94 540 


52 


9 


67 374 


72 841 


27159 


94 533 


51 


io 


67 398 


72 872 


27128 


94 526 


50 


11 


67 421 


72 902 


27 098 


94 519 


49 


12 


67 445 


72 932 


27 068 


94 513 


48 


13 


67 468 


72 963 


27 037 


94 506 


47 


14 


67 492 


72 993 


27 007 


94 499 


46 


15 


67 515 


73 023 


26 977 


94 492 


45 


16 


67 539 


73 054 


26 946 


94 485 


44 


17 


67 562 


73 084 


26 916 


94 479 


43 


18 


67 586 


73 114 


26 886 


94 472 


42 


19 


67 609 


73 144 


26 856 


94 465 


41 


20 


67 633 


73 175 


26 825 


94 458 


40 


21 


67 656 


73 205 


26 795 


94 451 


39 


22 


67 680 


73 235 


26 765 


94 445 


3S 


23 


67 703 


73 265 


26 735 


94 438 


37 


24 


67 726 


73 295 


26 705 


94 431 


36 


25 


67 750 


73 326 


26 674 


94 424 


35 


26 


67 773 


73 356 


26 644 


94 417 


34 


27 


67 796 


73 386 


26 614 


94 410 


33 


28 


67 820 


73 416 


26 584 


94 404 


32 


29 


67 843 


73 446 


26 554 


94 397 


31 


30 


67 866 


73 476 


26 524 


94 390 


30 


31 


67 890 


73 507 


26 493 


94 383 


29 


32 


67 913 


73 537 


26 463 


94 376 


28 


33 


67 936 


73 567 


26 433 


94 369 


27 


34 


67 959 


73 597 


26 403 


94 362 


26 


35 


67 982 


73 627 


26 373 


94 355 


25 


36 


68 006 


73 657 


26 343 


94 349 


24 


37 


68 029 


73 687 


26 313 


94 342 


23 


38 


68 052 


73 717 


26 283 


94 335 


22 


39 


68 075 


73 747 


26 253 


94 328 


21 


40 


68 098 


73 777 


26 223 


94 321 


20 


41 


68 121 


73 807 


26193 


94 314 


19 


42 


68 144 


73 837 


26163 


94 307 


18 


43 


68167 


73 867 


26133 


94 300 


17 


44 


68190 


73 897 


26103 


94 293 


16 


45 


68 213 


73 927 


26 073 


94 286 


15 


46 


68 237 


73 957 


26 043 


94 279 


14 


47 


68 260 


73 987 


26 013 


94 273 


13 


48 


68 2S3 


74 017 


25 983 


94 266 


12 


49 


68 305 


74 047 


25 953 


94 259 


11 


50 


68 328 


74 077 


25 923 


94 252 


10 


51 


68 351 


74 107 


25 893 


94 245 


9 


52 


68 374 


74137 


25 863 


94 238 


8 


53 


68 397 


74 166 


25 834 


94 231 


7 


54 


68 420 


74196 


25 804 


94 224 


6 


55 


68 443 


74 226 


25 774 


94 217 


5 


56 


68 466 


74 256 


25 744 


94 210 


4 


57 


68 489 


74 286 


25 714 


94 203 


3 


58 


68 512 


74 316 


25 684 


94196 


2 


59 


68 534 


74 345 


25 655 


94 189 


1 


60 


68 557 


74 375 


25 625 


94 182 







9 


9 


10 


9 




t 


log cos 


log cot 


log tan 


log sin 


t 



62° 



6r 



42 




29° 






t 


log sin 


log tan 


log cot 


log cos 


f 




9 

68 557 


9 

74 375 


io 

25 625 


9 

94 182 




o 


60 


1 


68 580 


74 405 


25 595 


94 175 


59 


2 


68 603 


74 435 


25 565 


94168 


5S 


3 


68 625 


74 465 


25 535 


94 161 


57 


4 


68 648 


74 494 


25 506 


94154 


56 


5 


68 671 


74 524 


25 476 


94147 


55 


6 


68 694 


74 554 


25 446 


94 140 


54 


7 


68 716 


74 583 


25 417 


94 133 


53 


8 


68 739 


74 613 


25 387 


94 126 


52 


9 


68 762 


74 643 


25 357 


94 119 


51 


10 


68 784 


74 673 


25 327 


94112 


50 


11 


6SS07 


74 702 


25 298 


94 105 


49 


12 


68 829 


74 732 


25 268 


94 098 


48 


13 


68 852 


74 762 


25 238 


94 090 


47 


14 


68 875 


74 791 


25 209 


94 083 


46 


15 


68 897 


74 821 


25 179 


94 076 


45 


16 


68 920 


74 851 


25 149 


94 069 


44 


17 


68 942 


74 880 


25 120 


94 062 


43 


18 


68 965 


74 910 


25 090 


94 055 


42 


19 


6S9S7 


74 939 


25 061 


94 048 


41 


20 


69 010 


74 969 


25 031 


94 041 


40 


21 


69 032 


74 99S 


25 002 


94 034 


39 


22 


69 055 


75 028 


24 972 


94 027 


38 


23 


69 077 


75 05S 


24 942 


94 020 


37 


24 


69 100 


75 087 


24 913 


94 012 


36 


25 


69 122 


75 117 


24 883 


94 005 


35 


26 


69 144 


75 146 


24 854 


93 998 


34 


27 


69 167 


75 176 


24 824 


93 991 


33 


28 


69 1S9 


75 205 


24 795 


93 984 


32 


29 


69 212 


75 235 


24765 


93 977 


31 


30 


69 234 


75 264 


24 736 


93 970 


30 


31 


69 256 


75 294 


24 706 


93 963 


29 


32 


69 279 


75 323 


24 677 


93 955 


28 


33 


69 301 


75 353 


24 647 


93 948 


27 


34 


69 323 


75 3S2 


24 618 


93 941 


26 


35 


69 345 


75 411 


24 589 


93 934 


25 


36 


69 368 


75 441 


24 559 


93 927 


24 


37 


69 390 


75 470 


24 530 


93 920 


23 


38 


69 412 


75 500 


24 500 


93 912 


22 


39 


69 434 


75 529 


24 471 


93 905 


21 


40 


69 456 


75 558 


24 442 


93S9S 


20 


41 


69 479 


75 588 


24 412 


93 891 


19 


42 


69 501 


75 617 


24 383 


93 884 


18 


43 


69 523 


75 647 


24 353 


93 S76 


17 


44 


69 545 


75 676 


24 324 


93 869 


16 


45 


69 567 


75 705 


24 295 


93 862 


15 


46 


69 5S9 


75 735 


24 265 


93 855 


14 


47 


69 611 


75 764 


24 236 


93 847 


13 ' 


4S 


69 633 


75 793 


24 207 


93 840 


12 


49 


69 655 


75S22 


24 178 


93 833 


11 


50 


69 677 


75 852 


24 148 


93 826 


10 


51 


69 699 


75S81 


24 119 


93 819 


9 


52 


69 721 


75 910 


24 090 


93 811 


8 


53 


69 743 


75 939 


24 061 


93 804 • 


7 


54 


69 765 


75 969 


24 031 


93 797 


6 


55 


69 7S7 


75 998 


24 002 


93 7S9 


5 


56 


69 809 


76 027 


23 973 


93 782 


4 


57 


69 831 


76 056 


23 944 


93 775 


3 


58 


69S53 


76 086 


23 914 


93 768 


2 


59 


69S75 


76115 


23SS5 


93 760 


1 


60 


69 897 


76144 


23 856 


93 753 







9 


9 


IO 


9 




t 


log cos 


log cot 


log tan 


log sin- 


t 







30° 








t 


log sin 


log tan 


log cot 


log cos 


/ 






9 


9 


IO 


9 










o 


69 897 


76 144 


23 856 


93 753 


60 




1 


69 919 


76173 


23 827 


93 746 


59 




2 


69 941 


76 202 


23 798 


93 738 


58 




3 


69 963 


76 231 


23 769 


93 731 


57 




4 


69 984 


76 261 


23 739 


93 724 


56 




5 


70 006 


76 290 


23 710 


93 717 


55 




6 


70 02S 


76 319 


23 681 


93 709 


54 




7 


70 050 


76 348 


23 652 


93 702 


53 




8 


70 072 


76 377 


23 623 


93 695 


52 




9 


70 093 


76 406 


23 594 


93 687 


51 




10 


70115 


76 435 


23 565 


93 680 


50 




11 


70137 


76 464 


23 536 


93 673 


49 




12 


70159 


76 493 


23 507 


93 665 


48 




13 


70180 


76 522 


23 478 


93 658 


47 




14 


70 202 


76 551 


23 449 


93 650 


46 




15 


70 224 


76 580 


23 420 


93 643 


45 




16 


70 245 


76 609 


23 391 


93 636 


44 




17 


70 267 


76 639 


23 361 


93 628 


43 




18 


70 288 


76 668 


23 332 


93 621 


42 




19 


70 310 


76 697 


23 303 


93 614 


41 




20 


70 332 


76 725 


23 275 


93 606 


40 




21 


70 353 


76 754 


23 246 


93 599 


39 




22 


70 375 


76 783 


23 217 


93 591 


38 




23 


70 396 


76 812 


23 188 


93 584 


37 




24 


70 418 


76 841 


23 159 


93 577 


36 




25 


70 439 


76 870 


23 130 


93 569 


35 




26 


70 461 


76 899 


23 101 


93 562 


34 




27 


70 482 


76 928 


23 072 


93 554 


33 




28 


70 504 


76 957 


23 043 


93 547 


32 




29 


. W 525 


76 986 


23 014 


93 539 


31 




30 


70 547 


77 015 


22 985 


93 532 


30 




31 


70 568 


77 044 


22 956 


93 525 


29 




32 


70 590 


77 073 


22 927 


93 517 


28 




33 


70 611 


77101 


22 899 


93 510 


27 




34 


70 633 


77130 


22 870 


93 502 


26 




35 


70 654 


77159 


22 841 


93 495 


25 




36 


70 675 


771S8 


22 812 


93 487 


24 




37 


70 697 


77 217 


22 783 


93 480 


23 




38 


70 718 


77 246 


22 754 


93 472 


22 




39 


70 739 


77 274 


22 726 


93 465 


21 




40 


70 761 


77 303 


22 697 


93 457 


20 




41 


70 7S2 


77 332 


22 668 


93 450 


19 




42 


70 803 


77 361 


2 1 639 


93 442 


IS 




43 


70 824 


77 390 


22 610 


93 435 


17 




44 


70 846 


77 418 


22 582 


93 427 


16 




45 


70 867 


77 447 


22 553 


93 420 


15 




46 


70G88 


77 476 


22 524 


93 412 


14 




47 


70 909 


77 505 


22 495 


93 405 


13 




4S 


70 931 


77 533 


22 467 


93 397 


12 




49 


70 952 


77 562 


22 438 


93 390 


11 




50 


70 973 


77 591 


22 409 


93 382 


10 




51 


70 994 


77 619 


22 381 


93 375 


9 




52 


71 015 


77 648 


22 352 


93 367 


8 




53 


71 036 


77 677 


22 323 


93 360 


7 




54 


71 058 


77 706 


22 294 


93 352 


6 




55 


71079 


77 734 


22 266 


93 344 


5 




56 


71100 


77 763 


22 237 


93 337 


4 




57 


71121 


77 791 


22 209 


93 329 


3 




58 


71142 


77 820 


22 180 


93 322 


2 




59 


71163 


77S49 


22 151 


93 314 


1 




60 


71184 


77 877 


22 123 


93 307 









9 

log cos 


9 

log cot 


IO 

log tan 


9 

log sin 






t 


r 





60 c 



59 c 



3r 



f 


log sin 


log tan 


log cot 


log cos 


t 




9 

71184 


9 

77 877 


10 

22123 


9 

93 307 







60 


1 


71205 


77 906 


22 094 


93 299 


59 


2 


71226 


77 935 


22 065 


93 291 


58 


3 


71247 


77 963 


22 037 


93 284 


57 


4 


71268 


77 992 


22 008 


93 276 


56 


5 


71289 


78 020 


219S0 


93 269 


55 


6 


71310 


78 049 


21951 


93 261 


54 


7 


71331 


78 077 


21923 


93 253 


53 


S 


71352 


78 106 


21894 


93 246 


52 


9 


7"1 373 


78135 


21865 


93 238 


51 


10 


71393 


78163 


21837 


93 230 


50 


11 


71414 


78192 


21808 


93 223 


49 


12 


71435 


78 220 


21780 


93 215 


48 


13 


71456 


78 249 


21751 


93 207 


47 


14 


71477 


78 277 


21723 


93 200 


46 


15 


71498 


78 306 


21694 


93 192 


45 


16 


71519 


78 334 


21666 


93 184 


44 


17 


71539 


78 363 


21637 


93 177 


43 


18 


71560 


78 391 


21609 


93 169 


42 


19 


71581 


78 419 


21581 


93 161 


41 


20 


71602 


78 448 


21552 


93 154 


40 


21 


71622 


78 476 


21524 


93 146 


39 


22 


71643 


78 505 


21495 


93 138 


38 


23 


71664 


78 533 


21467 


93 131 


37 


24 


71685 


78 562 


21438 


93 123 


36 


25 


71705 


78 590 


21410 


93 115 


35 


26 


71726 


78 618 


21382 


93 108 


34 


27 


71747 


78 647 


21353 


93 100 


33 


28 


71767 


78 675 


21325 


93 092 


32 


29 


71788 


78 704 


21296 


93 084 


31 


30 


71809 


78 732 


21268 


93 077 


30 


31 


71829 


78 760 


21240 


93 069 


29 


32 


71S50 


78 789 


21211 


93 061 


28 


33 


71870 


78 817 


21183 


93 053 


27 


34 


71891 


78 845 


21155 


93 046 


26 


35 


71911 


78 874 


21126 


93 038 


25 


36 


71932 


78 902 


21098 


93 030 


24 


37 


71952 


78 930 


21070 


93 022 


23 


38 


71973 


78 959 


21041 


93 014 


22 


39 


71994 


78 9S7 


21013 


93 007 


21 


40 


72 014 


79 015 


20 985 


92 999 


20 


41 


72 034 


79 043 


20 957 


92 991 


19 


42 


72 055 


79 072 


20 928 


92 983 


18 


43 


72 075 


79100 


20 900 


92 976 


17 


44 


72 096 


7912S 


20 872 


92 968 


16 


45 


72 116 


79156 


20 844 


92 960 


15 


46 


72137 


79185 


20 815 


92 952 


14 


47 


72157 


79 213 


20 787 


92 944 


13 


48 


72177 


79 241 


20 759 


92 936 


12 


49 


72198 


79 269 


20 731 


92 929 


11 


50 


72 218 


79 297 


20 703 


92 921 


IO 


51 


72 238 


79 326 


20 674 


92 913 


9 


52 


72 259 


79 354 


20 646 


92 905 


8 


53 


72 279 


79 382 


20 618 


92 897 


7 


54 


72 299 


79 410 


20 590 


92 889 


6 


55 


72 320 


79 43S 


20 562 


92 881 


5 


56 


72 340 


79 466 


20 534 


92 874 


4 


57 


72 360 


79 495 


20 505 


92 866 


3 


58 


72 381 


79 523 


20 477 


92 858 


2 


59 


72 401 


79 551 


20 449 


92 850 


1 


60 


72 421 


79 579 


20 421 


92 842 







9 

log cos 


9 

log cot 


io 

log tan 


9 

log sin 




f 


t 







32° 




43 


f 


log sin 


log tan 


log cot 


log cos 


r 




9 

72 421 


9 

79 579 


10 

20 421 


9 

92 842 







60 


1 


72 441 


79 607 


20 393 


92 834 


59 


2 


72 461 


79 635 


20 365 


92 826 


58 


3 


72 482 


79 663 


20 337 


92 818 


57 


4 


72 502 


79 691 


20 309 


92 810 


56 


5 


72 522 


79 719 


20 281 


92S03 


55 


6 


72 542 


79 747 


20 253 


92 795 


54 


7 


72 562 


79 776 


20 224 


92 787 


53 


S 


72 582 


79 804 


20196 


92 779 


52 


9 


72 602 


79 832 


20168 


92 771 


51 


IO 


72 622 


79 860 


20140 


92 763 


50 


11 


72 643 


79 888 


20112 


92 755 


49 


12 


72 663 


79 916 


20 084 


92 747 


48 


13 


72 683 


79 944 


20 056 


92 739 


47 


14 


72 703 


79 972 


20 028 


92 731 


46 


15 


72 723 


80 000 


20 000 


92 723 


45 


16 


72 743 


80 028 


19 972 


92 715 


44 


17 


72 763 


80 056 


19 944 


92 707 


43 


18 


72 783 


80 084 


19 916 


92 699 


42 


19 


72 803 


80112 


19 888 


92 691 


41 


20 


72 823 


80140 


19 860 


92 683 


40 


21 


72 843 


80168 


19 832 


92 675 


39 


22 


72 863 


80195 


19 805 


92 667 


38 


23 


72 883 


80 223 


19 777 


92 659 


37 


24 


72 902 


80 251 


19 749 


92 651 


36 


25 


72 922 


80 279 


19 721 


92 643 


35 


26 


72 942 


80 307 


19 693 


92 635 


34 


27 


72 962 


80 335 


19 665 


92 627 


33 


28 


72 982 


80 363 


19 637 


92 619 


31 


29 


73 002 


80 391 


19 609 


92 611 


31 


30 


73 022 


80 419 


19 581 


92 603 


30 


31 


73 041 


80 447 


19 553 


92 595 


29 


32 


73 061 


80 474 


19 526 


92 587 


28 


33 


73 081 


80 502 


19 498 


92 579 


27 


34 


73101 


80 530 


19 470 


92 571 


26 


35 


73 121 


80 558 


19 442 


92 563 


25 


36 


73 140 


80 586 


19 414 


92 555 


24 


37 


73 160 


80 614 


19 386 


92 546 


23 


38 


73180 


80 642 


19 358 


92 538 


22 


39 


73 200 


80 669 


19 331 


92 530 


21 


40 


73 219 


80 697 


19 303 


92 522 


20 


41 


73 239 


80 725 


19 275 


92 514 


19 


42 


73 259 


80 753 


19 247 


92 506 


18 


43 


73 278 


80 781 


19 219 


92 498 


17 


44 


73 29S 


80 808 


19192 


92 490 


16 


45 


73 318 


80 836 


19164 


92 482 


15 


46 


73 337 


80 864 


19136 


92 473 


14 


47 


73 357 


80 892 


19108 


92 465 


13 


48 


73 377 


80 919 


19 081 


92 457 


12 


49 


73 396 


80 947 


19 053 


92 449 


11 


50 


73 416 


8Q975 


19 025 


92 441 


10 


51 


73 435 


81003 


18 997 


92 433 


9 


52 


73 455 


81030 


18 970 


92 425 


8 


53 


73 474 


8105S 


18 942 


92 416 


7 


54 


73 494 


81086 


18 914 


92 408 


6 


55 


73 513 


81113 


18 887 


92 400 


5 


56 


73 533 


81141 


18 859 


92 392 


4 


57 


73 552 


81169 


18 831 


92 384 


3 


58 


73 572 


81196 


18 804 


92 376 


2 


59 


73 591 


81224 


18 776 


92 367 


1 


60 


73 611 


81252 


18 74S 


92 359 


O 




9 

log cos 


9 

log cot 


IO 

log tan 


9 

log sin 




t 


t 



58 c 



57 c 



44 




33° 






t 


log sin 


log tan 


log cot 


log cos 


/ 




9 

73 611 


9 

81252 


10 

18 748 


9 

92 359 




o 


60 


1 


73 630 


81279 


18 721 


92 351 


59 


2 


73 650 


81307 


18 693 


92 343 


58 


3 


73 669 


81335 


18 665 


92 335 


57 


4 


73 689 


81362 


18 638 


92 326 


56 


5 


73 708 


81390 


18 610 


92 318 


55 


6 


73 727 


81418 


18 582 


92 310 


54 


7 


73 747 


81445 


18 555 


92 302 


53 


8 


73 766 


81473 


18 527 


92 293 


52 


9 


73 785 


81500 


18 500 


92 285 


51 


10 


73 805 


81528 


18 472 


92 277 


50 


11 


73 824 


81556 


18 444 


92 269 


49 


12 


73 843 


81583 


18 417 


92 260 


48 


13 


73 863 


81611 


18 389 


92 252 


47 


14 


73 882 


81638 


18 362 


92 244 


46 


15 


73 901 


81666 


18 334 


92 235 


45 


16 


73 921 


81693 


18 307 


92 227 


44 


17 


73 940 


81721 


18 279 


92 219 


43 


18 


73 959 


81748 


18 252 


92 211 


42 


19 


73 978 


81776 


18 224 


92 202 


41 


20 


73 997 


81803 


18 197 


92 194 


40 


21 


74 017 


81831 


18169 


92186 


39 


22 


74 036 


81858 


18142 


92 177 


38 


23 


74 055 


81886 


18 114 


92 169 


37 


24 


74 074 


81913 


18 087 


92 161 


36 


25 


74 093 


81941 


18 059 


92 152 


35 


26 


74113 


81968 


18 032 


92144 


34 


27 


74132 


81996 


18 004 


92 136 


33 


28 


74151 


82 023 


17 977 


92 127 


32 


29 


74170 


82 051 


17 949 


92119 


31 


30 


74189 


82 078 


17 922 


92111 


30 


31 


74 208 


82106 


17 894 


92 102 


29 


32 


74 227 


82 133 


17 867 


92 094 


28 


33 


74 246 


82 161 


17 839 


92 086 


27 


34 


74 265 


82 188 


17 812 


92 077 


26 


35 


74 284 


82 215 


17 785 


92 069 


25 


36 


74 303 


82 243 


17 757 


92 060 


24 


37 


74 322 


82 270 


17 730 


92 052 


23 


38 


74 341 


82 298 


17 702 


92 044 


22 


39 


74 360 


82 325 


17 675 


92 035 


21 


40 


74 379 


82 352 


17 648 


92 027 


20 


41 


74 398 


82 380 


17 620 


92 018 


19 


42 


74 417 


82 407 


17 593 


92 010 


18 


43 


74 436 


82 435 


17 565 


92 002 


17 


44 


74 455 


82 462 


17 538 


91993 


16 


45 


74 474 


82 489 


17 511 


91985 


15 


46 


74 493 


82 517 


17 483 


91976 


14 


47 


74 512 


82 544 


17 456 


91968 


13 


48 


74 531 


82 571 


17 429 


91959 


12 


49 


74 549 


82 599 


17 401 


91951 


11 


50 


74 568 


82 626 • 


17 374 


91942 


10 


51 


74 587 


82 653 


17 347 


91934 


9 


52 


74 606 


82 681 


17 319 


91925 


8 


53 


74 625 


82 708 


17 292 


91917 


7. 


54 


74 644 


82 735 


17 265 


91908 


6 


55 


74 662 


82 762 


17 238 


91900 


5 


56 


74 681 


82 790 


17 210 


91891 


4 


57 


74 700 


82 817 


17183 


91883 


3 


58 


74 719 


82 844 


17156 


91874 


2 


59 


74 737 


82 871 


17129 


91866 


1 


60 


74 756 


82 899 


17101 


91857 







9 


9 


10 


9 




t 


log cos 


log cot 


log tan 


log sin 


j 



34 c 



r 


log sin 


log tan log cot 


log cos 


/ 




9 

74 756 


9 10 

82 899 17101 


9 

91857 







60 


1 


74 775 


82 926 17 074 


91849 


59 


2 


74 794 


82 953 17 047 


91840 


58 


3 


74 812 


82 980 17 020 


91832 


57 


4 


74 831 


83 008 16 992 


91823 


56 


5 


74 850 


83 035 16 965 


91815 


55 


6 


74 868 


83 062 16 938 


91806 


54 


7 


74 887 


83 089 16 911 


91798 


53 


8 


74 906 


83 117 16 883 


91789 


52 


9 


74 924 


83 144 16 856 


91781 


51 


10 


74 943 


83 171 16 829 


91772 


50 


11 


74 961 


83 198 16 802 


91763 


49 


12 


74 980 


83 225 16 775 


91755 


48 


13 


74 999 


83 252 16 748 


91746 


47 


14 


75 017 


83 280 16 720 


91738 


46 


15 


75 036 


83 307 16 693 


91729 


45 


16 


75 054 


83 334 16 666 


91720 


44 


17 


75 073 


83 361 16 639 


91712 


43 


18 


75 091 


83 388 16 612 


91703 


42 


19 


75 110 


83 415 16 585 


91695 


41 


20 


75 128 


83 442 16 558 


91686 


40 


21 


75 147 


83 470 16 530 


91677 


39 


22 


75 165 


83 497 16 503 


91669 


38 


23 


75 184 


83 524 16 476 


91660 


37 


24 


75 202 


83 551 16 449 


91651 


36 


25 


75 221 


83 578 16 422 


91643 


35 


26 


75 239 


83 605 16 395 


91634 


34 


27 


75 258 


83 632 16 368 


91625 


33 


28 


75 276 


83 659 16 341 


91617 


32 


29 


75 294 


83 686 16 314 


91608 


31 


30 

31 


75 313 


83 713 16 287 


91599 


30 


75 331 


83 740 16 260 


91 591 


29 


32 


75 350 


83 768 16 232 


91582 


28 


33 


75 368 


83 795 16 205 


91 573 


27 


34 


75 386 


83 822 16178 


91565 


26 


35 


75 405 


83 849 16 151 


91556 


25 


36 


75 423 


83 876 16124 


91547 


24 


37 


75 441 


83 903 16 097 


91538 


23 


38 


75 459 


83 930 16 070 


91530 


22 


39 


75 478 


83 957 16 043 


91521 


21 


40 


75 496 


83 984 16 016 


91512 


20 


41 


75 514 


84 011 15 989 


91504 


19 


42 


75 533 


84 038 15 962 


91495 


18 


43 


75 551 


84 065 15 935 


91486 


17 


44 


75 569 


84 092 15 908 


91477 


16 


45 


75 587 


84119 15 881 


91469 


15 


46 


75 605 


84146 15 854 


91460 


14 


47 


75 624 


84173 15 827 


91451 


13 


48 


75 642 


84 200 15 800 


91442 


12 


49 


75 660 


84 227 15 773 


91433 


11 


50 


75 678 


84 254 15 746 


91425 


10 


51 


75 696 


84 280 15 720 


91416 


9 


52 


75 714 


84 307 15 693 


91407 


8 


53 


75 733 


84 334 15 666 


91398 


7 


54 


75 751 


84 361 15 639 


91389 


6 


55 


75 769 


84 388 15 612 


91 381 


5 


56 


75 787 


84 415 15 585 


91372 


4 


57 


75 805 


84 442 15 558 


91363 


3 


58 


75 823 


84 469 15 531 


91354 


2 


59 


75 841 


84 496 15 504 


91345 


1 


60 


75 859 


84 523 15 477 


91336 







9 

log oos 


9 10 

log cot log tan 


9 

log sin 




t 


r I 



56 c 



55 c 



35 c 



f 


log sin 


log tan 


log cot 


log cos 


t 




9 

75 859 


9 

84 523 


10 

15 477 


9 

91336 







60 


1 


75 877 


84 550 


15 450 


91328 


59 


2 


75 895 


84 576 


15 424 


91319 


58 


3 


75 913 


84 603 


15 397 


91310 


57 


4 


75 931 


84 630 


15 370 


91301 


56 


5 


75 949 


84 657 


15 343 


91292 


55 


6 


75 967 


84 684 


15 316 


91283 


54 


7 


75 985 


84 711 


15 289 


91274 


53 


8 


76 003 


84 738 


15 262 


91 266 


52 


9 


76 021 


84 764 


15 236 


91257 


51 


10 


76 039 


84 791 


15 209 


91248 


50 


11 


76 057 


84 818 


15 182 


91239 


49 


12 


76 075 


84 845 


15 155 


91230 


48 


13 


76 093 


84 872 


15 128 


91 221 


47 


14 


76111 


84 899 


15 101 


91212 


46 


15 


76129 


84 925 


15 075 


91203 


45 


16 


76146 


84 952 


15 048 


91194 


44 


17 


76164 


84 979 


15 021 


91 185 


43 


18 


76 182 


85 006 


14 994 


91176 


42 


19 


76 200 


85 033 


14 967 


91167 


41 


20 


76 218 


85 059 


14 941 


91158 


40 


21 


76 236 


85 086 


14 914 


91149 


39 


22 


76 253 


85 113 


14 887 


91141 


38 


23 


76 271 


85 140 


14 860 


91132 


37 


24 


76 289 


85 166 


14 834 


91123 


36 


25 


76 307 


85 193 


14 807 


91114 


35 


26 


76 324 


85 220 


14 780 


91105 


34 


27 


76 342 


85 247 


14 753 


91096 


33 


28 


76 360 


85 273 


14 727 


91087 


32 


29 


76 378 


85 300 


14 700 


91078 


31 


30 


76 395 


85 327 


14 673 


91069 


30 


31 


76 413 


85 354 


14 646 


91060 


29 


32 


76 431 


85 380 


14 620 


91051 


28 


33 


76 448 


85 407 


14 593 


91042 


27 


34 


76 466 


85 434 


14 566 


91033 


26 


35 


76484 


85 460 


14 540 


91023 


25 


36 


76 501 


85 487 


14 513 


91014 


24 


37 


76 519 


85 514 


14 486 


91005 


23 


38 


76 537 


85 540 


14 460 


90 996 


22 


39 


76 554 


85 567 


14 433 


90 987 


21 


40 


76 572 


85 594 


14 406 


90 978 


20 


41 


76 590 


85 620 


14 380 


90 969 


19 


42 


76 607 


85 647 


14 353 


90 960 


18 


43 


76 625 


85 674 


14 326 


90 951 


17 


44 


76 642 


S5 700 


14 300 


90 942 


16 


45 


76 660 


85 727 


14 273 


90 933 


15 


46 


76 677 


85 754 


14 246 


90 924 


14 


47 


76 695 


85 780 


14 220 


90 915 


13 


48 


76 712 


85 807 


14193 


90 906 


12 


49 


76 730 


85 834 


14 166 


90 896 


11 


50 


76 747 


85 860 


14140 


90 887 


10 


51 


76 765 


85 887 


14 113 


90 878 


9 


52 


76 782 


85 91'3 


14 087 


90 869 


8 


53 


76 800 


85 940 


14 060 


90 860 


7 


54 


76 817 


85 967 


14 033 


90 851 


6 


55 


76 835 


85 993 


14 007 


90 842 


5 


56 


76 852 


86 020 


13 980 


90 832 


4 


57 


76 870 


86 046 


13 954 


90 823 


3 


58 


76 887 


86 073 


13 927 


90 814 


2 


59 


76 904 


86 100 


13 900 


90 805 


1 


60 


76 922 


86126 


13 874 


90 796 







9 

log COS 


9 

log cot 


10 

log tan 


9 

log sin 




r 


t 







36° 




45 


r 


log sin 


log tan 


log cot 


log cos 


t 




9 

76 922 


9 

86126 


10 

13 874 


9 

90 796 







60 


1 


76 939 


86 153 


13 847 


90 787 


59 


2 


76 957 


86 179 


13 821 


90 777 


58 


3 


76 974 


86 206 


13 794 


90 768 


57 


4 


76 991 


86 232 


13 768 


90 759 


56 


5 


77 009 


86 259 


13 741 


90 750 


55 


6 


77 026 


86 285 


13 715 


90 741 


54 


7 


77 043 


86 312 


13 688 


90 731 


53 


8 


77 061 


86 338 


13 662 


90 722 


52 


9 


77 078 


86 365 


13 635 


90 713 


51 


10 


77 095 


86 392 


13 608 


90 704 


50 


11 


77 112 


86 418 


13 582 


90 694 


49 


12 


77130 


86 445 


13 555 


90 685 


48 


13 


77147 


86 471 


13 529 


90 676 


47 


14 


77 164 


86 498 


13 502 


90 667 


46 


15 


77181 


86 524 


13 476 


90 657 


45 


16 


77199 


86 551 


13 449 


90 648 


44 


17 


77 216 


86 577 


13 423 


90 639 


43 


18 


77 233 


86 603 


13 397 


90 630 


42 


19 


77 250 


86 630 


13 370 


90 620 


41 


20 


77 268 


86 656 


13 344 


90 611 


40 


21 


77 285 


86 683 


13 317 


90 602 


39 


22 


77 302 


86 709 


13 291 


90 592 


38 


23 


77 319 


86 736 


13 264 


90 583 


37 


24 


77 336 


86 762 


13 238 


90 574 


36 


25 


77 353 


86 789 


13 211 


90 565 


35 


26 


77 370 


86 815 


13 185 


90 555 


34 


27 


77 387 


86 842 


13 158 


90 546 


33 


28 


77 405 


86 868 


13 132 


90 537 


32 


29 


77 422 


86 894 


13 106 


90 527 


31 


30 


77 439 


86 921 


13 079 


90 518 


30 


31 


77 456 


86 947 


13 053 


90 509 


29 


32 


77 473 


86 974 


13 026 


90 499 


28 


33 


77 490 


87 000 


13 000 


90 490 


27 


34 


77 507 


87 027 


12 973 


90 480 


26 


35 


77 524 


87 053 


12 947 


90 471 


25 


36 


77 541 


87 079 


12 921 


90 462 


24 


37 


77 558 


87106 


12 894 


90 452 


23 


38 


77 575 


87132 


12 868 


90 443 


22 


39 


77 592 


87158 


12 842 


90 434 


21 


40 


77 609 


87185 


12 815 


90 424 


20 


41 


77 626 


87 211 


12 789 


90 415 


19 


42 


77 643 


87 238 


12 762 


90 405 


18 


43 


77 660 


87 264 


12 736 


90 396 


17 


44 


77 677 


87 290 


12 710 


90 386 


16 


45 


77 694 


87 317 


12 683 


90 377 


15 


46 


77 711 


87 343 


12 657 


90 368 


14 


47 


77 728 


87 369 


12 631 


90 358 


13 


48 


77 744 


87 396 


12 604 


90 349 


12 


49 


77 761 


87 422 


12 578 


90 339 


11 


50 


77 778 


87 448 


12 552 


90 330 


10 


51 


77 795 


87 475 


12 525 


90 320 


9 


52 


77 812 


87 501 


12 499 


90 311 


8 


53 


77 829 


87 527 


12 473 


90 301 


7 


54 


77 846 


87 554 


12 446 


90 292 


6 


55 


77 862 


87 580 


12 420 


90 282 


5 


56 


77 879 


87 606 


12 394 


90 273 


4 


57 


77 896 


87 633 


12 367 


90 263 


3 


58 


77 913 


87 659 


12 341 


90 254 


2 


59 


77 930 


87 685 


12 315 


90 244 


1 


60 


77 946 


87 711 


12 289 


90 235 







9 


9 


io 


9 




r 


log cos 


log cot 


log tan 


log sin 


t 



54 c 



53 c 



46 




37° 






t 


log sin 


log tan 


log cot 


log cos 


t 




9 

77 946 


9 

87 711 


10 

12 289 


9 

90 235 




o 


60 


1 


77 963 


87 738 


12 262 


90 225 


59 


2 


77 980 


87 764 


12 236 


90 216 


58 


3 


77 997 


87 790 


12 210 


90 206 


57 


'4 


78 013 


87 817 


12183 


90197 


56 


5 


78 030 


87 843 


12157 


90187 


55 


6 


78 047 


87 869 


12 131 


90178 


54 


7 


78 063 


87 895 


12 105 


90168 


53 


8 


78 080 


87 922 


12 078 


90 159 


52 


9 


78 097 


87 948 


12 052 


90149 


51 


10 


78113 


87 974 


12 026 


90139 


50 


11 


78130 


88 000 


12 000 


90130 


49 


12 


78 147 


88 027 


11973 


90120 


48 


13 


78 163 


88 053 


11947 


90111 


47 


14 


78 180 


88 079 


11921 


90 101 


46 


15 


78 197 


88 105 


11895 


90 091 


45 


16 


78 213 


88 131 


11869 


90 082 


44 


17 


78 230 


88158 


11842 


90 072 


43 


18 


78 246 


88 184 


11816 


90 063 


42 


19 


78 263 


S8 210 


11790 


90 053 


41 


20 


78 280 


88 236 


11764 


90 043 


40 


21 


78 296 


88 262 


11738 


90 034 


39 


22 


78 313 


88 289 


11711 


90 024 


38 


23 


78 329 


88 315 


11685 


90 014 


37 


24 


7S346 


88 341 


11659 


90 005 


36 


25 


78 362 


88 367 


11633 


89 995 


35 


26 


78 379 


88 393 


11607 


89 985 


34 


27 


78 395 


88 420 


11580 


89 976 


33 


28 


78 412 


88 446 


11554 


89 966 


32 


29 


78 428 


88 472 


11528 


89 956 


31 


30 


78 445 


88 498 


11502 


89 947 


30 


31 


78 461 


8S524 


11476 


89 937 


29 


32 


78 478 


88 550 


11450 


89 927 


28 


33 


78 494 


88 577 


11423 


89 918 


27 


34 


78 510 


88 603 


11397 


89 908 


26 


35 


78 527 


88 629 


11371 


89 898 


25 


36 


78 543 


88 655 


11345 


89 888 


24 


37 


78 560 


88 681 


11319 


89 879 


23 


38 


78 576 


88 707 


11293 


89 869 


22 


39 


78 592 


88 733 


11267 


89 859 


21 


40 


78 609 


88 759 


11241 


89 849 


20 


41 


78 625 


88 786 


11214 


89 840 


19 


42 


78 642 


88S12 


11188 


89 830 


18 


43 


78 658 


88 838 


11162 


89 820 


17 


44 


78 674 


88 864 


11136 


89 810 


16 


45 


78 691 


88 890 


11110 


89 801 


15 


46 


78 707 


88 916 


11084 


89 791 


14 


47 


78 723 


88 942 


11058 


89 781' 


13 


48 


78 739 


8S96S 


11 032 


89 771 


12 


49 


78 756 


88 994 


11006 


89 761 


11 


50 


78 772 


89 020 


10 980 


89 752 


10 


51 


78 788 


89 046 


10 954 


89 742 


9 


52 


78 805 


89 073 


10 927 


89 732 


8 


53 


78 821 


89 099 


10 901 


89 722 


-7 


54 


78 837 


89125 


10 875 


89 712 


6 


55 


78 853 


89 151 


10 849 


89 702 


5 


56 


78 869 


89 177 


10 823 


89 693 


4 


57 


78 886 


89 203 


10 797 


89 683 


3 


58 


78 902 


89 229 


10 771 


89 673 


2 


59 


78 918 


89 255 


10 745 


89 663 


1 


60 


78 934 


S9 2S1 


10 719 


89 653 


O 




9 

log cos 


9 

log cot 


io 

log tan 


9 

log sin 




t 


- t 



38 c 



t 


log sin 


log tan 


log cot 


log cos 


/ 




9 

78 934 


9 

89 281 


10 

10 719 


9 

89 653 




o 


60 


1 


78 950 


89 307 


10 693 


89 643 


59 


2 


78 967 


89 333 


10 667 


89 633 


58 


3 


78 983 


89 359 


10 641 


89 624 « 


57 


4 


78 999 


S9 3S5 


10 615 


89 614 


56 


5 


79 015 


89 411 


10 5S9 


89 604 


55 


6 


79 031 


89 437 


10 563 


89 594 


54 


7 


79 047 


S9 463 


10 537 


89 584 


53 


8 


79 063 


89 489 


10 511 


89 574 


52 


9 


79 079 


89 515 


10 485 


89 564 


51 


10 


79 095 


89 541 


10 459 


89 554 


50 


11 


79 111 


89 567 


10 433 


89 544 


49 


12 


79 128 


89 593 


10 407 


89 534 


48 


13 


79144 


89 619 


10 381 


89 524 


47 


14 


79160 


89 645 


10 355 


89 514 


46 


15 


79 176 


. 89 671 


10 329 


89 504 


45 


16 


79192 


89 697 


10 303 


89 495 


44 


17 


79 208 


89 723 


10 277 


89 485 


43 


18 


79 224 


89 749 


10 251 


89 475 


42 


19 


79 240 


89 775 


10 225 


89 465 


41 


20 


79 256 


89 801 


10 199 


89 455 


40 


21 


79 272 


89 827 


10173 


89 445 


39 


22 


79 288 


89 853 


10147 


89 435 


38 


23 


79 304 


89 879 


10 121 


89 425 


37 


24 


79 319 


89 905 


10 095 


89 415 


36 


25 


79 335 


89 931 


10 069 


89 405 


35 


26 


79 351 


89 957 


10 043 


89 395 


34 


27 


79 367 


89 983 


10 017 


89 385 


33 


28 


79 383 


90 009 


09 991 


89 375 


32 


29 


79*399 


90 035 


09 965 


89 364 


31 


30 


79'415 


90 061 


09 939 


89 354 


30 


31 


79 431 


90 086 


09 914 


89 344 


29 


32 


79 447 


90 112 


09 888 


89 334 


28 


33 


79 463 


90138 


09 862 


89 324 


27 


34 


79 478 


90164 


09 836 


89 314 


26 


35 


79 494 


90190 


09 810 


89 304 


25 


36 


79 510 


90 216 


09 784 


89 294 


24 


37 


79 526 


90 242 


09 758 


89 284 


23 


38 


79 542 


90 26S 


09 732 


89 274 


22 


39 


79 558 


90 294 


09 706 


S9 264 


21 


40 


79 573 


90 320 


09 680 


89 254 


20 


41 


79 589 


90 346 


09 654 


89 244 


19 


42 


79 605 


90 371 


09 629 


89 233 


IS 


43 


79 621 


90 397 


09 603 


89 223 


17 


44 


79 636 


90 423 


09 577 


89 213 


16 


45 


79 652 


90 449 


09 551 


89 203 


15 


46 


79 668 


90 475 


09 525 


89193 


14 


47 


79 684 


90 501 


09 499 


89 183 


13 


48 


79 699 


90 527 


09 473 


89173 


12 


49 


79 715 


90 553 


09 447 


89162 


11 


50 


79 731 


90 578 


09 422 


89152 


10 


51 


79 746 


90 604 


09 396 


89142 


9 


52 


79 762 


90 630 


09 370 


S9 132 


8 


53 


79 77S 


90 656 


09 344 


89122 


7 


54 


79 793 


90 6S2 


09 318 


89112 


6 


55 


79 809 


90 708 


09 292 


89 101 


5 


56 


79 825 


90 734 


09 266 


89 091 


4 


57 


79 840 


90 759 


09 241 


89 081 


3 


58 


79 856 


90 785 


09 215 


89 071 


2 


59 


79 872 


90 811 


09 189 


89 060 


1 


60 


79 887 


90 837 


09 163 


89 050 


O 




9 


9 


10 


9 






r 


log COS 


log cot 


log tan 


log sin 


t 



52 c 



51 c 







39° 




t 


log sin 


log tan 


leg cot log cos 


t 




9 

79 8S7 


9 

90S37 


10 9 

09163 S9 050 







60 


1 


79 903 


90 863 


09137 S9 040 


59 


2 


79 91S 


90SS9 


09 111 89 030 


5S 


3 


79 934 


90 914 


09 086 S9 020 


57 


4 


79 950 


90 940 


09 060 89 009 


56 


5 


79 965 


90 966 


09 034 SS999 


55 


6 


79 981 


90 992 


09 00S 88 989 


54 


7 


79 996 


91018 


08 9S2 SS97S 


53 


S 


80 012 


91043 


OS 957 88 968 


52 


9 


80 027 


91069 


OS 931 SS958 


51 


10 


SO 043 


91095 


08 905 88 948 


50 


11 


80 058 


91121 


0SS79 88 937 


49 


12 


SO 074 


91147 


08 853 88 927 


4S 


13 


80 0S9 


91172 


08 82S 88 917 


47 


14 


SO 105 


91198 


0SS02 8S906 


46 


15 


SO 120 


91224 


08 776 88 896 


45 


16 


SO 136 


91250 


OS 750 88 886 


44 


17 


80151 


91276 


08 724 88 875 


43 


IS 


SO 166 


91301 


08 699 SSS65 


42 


19 


80 182 


91327 


08 673 8S85i 


41 


20 


80 197 


91 353 


OS 647 88 844 


40 


21 


80 213 


91379 


OS 621 88 834 


39 


22 


SO 228 


91404 


08 596 8S824 


38 


23 


80 244 


91430 


OS 570 88 813 


37 


24 


80 259 


91456 


OS 544 88S03 


36 


25 


80 274 


91482 


0S51S SS793 


35 


26 


SO 290 


91507 


08 493 88 782 


34 


27 


SO 305 


91533 


08 467 88 772 


33 


2S ' 


80 320 


91559 


08 441 88 761 


32 


29 


80 336 


91585 


08 415 88 751 


31 


30 


80 351 


91610 


08 390 88 741 


30 


31 


80 366 


91636 


OS 364 88 730 


29 


32 


80 382 


91662 


OS 338 88 720 


28 


33 


SO 397 


916SS 


OS 312 8S709 


27 


34 


80 412 


91713 


08 287 88 699 


26 


35 


80428 


91739 


08 261 S8 6S8 


25 


36 


80 443 


91765 


OS 235 SS678 


24 


37 


S0 45S 


91791 


OS 209 8S66S 


23 


38 


SO 473 


91816 


OS 184 8S657 


22 


39 


S0 4S9 


91842 


0S15S SS647 


21 


40 


80 504 


91868 


08132 88 636 


20 


41 


80 519 


91893 


08 107 88 626 


19 


42 


80 534 


91919 


08 081 88 615 


18 


43 


80 550 


91945 


OS 055 S8 605 


17 


44 


80 565 


91971 


08 029 88 594 


16 


45 


80 5S0 


91996 


08 004 88 584 


15 


46 


80 595 


92 022 


07 978 8S573 


14 


47 


80 610 


92 04S 


07 952 88 563 


13 


48 


SO 625 


92 073 


07 927 88 552 


12 


49 


SO 641 


92 099 


07 901 88 542 


11 


50 


80 656 


92125 


07 875 SS531 


10 


51 


80 671 


92 150 


07 850 88 521 


9 


52 


S0 6S6 


92 176 


07 824 88 510 


S 


53 


80 701 


92 202 


07 798 88 499 


7 


54 


80 716 


92 227 


07 773 8S4S9 


6 


55 


SO 731 


92 253 


07 747 88 478 


5 


56 


80 746 


92 279 


07 721 • SS 468 


4 


57 


80 762 


92 304 


07 696 88 457 


3 


58 


SO 777 


92 330 


07 670 8S447 


2 


59 


80 792 


92 356 


07 644 88 436 


1 


60 


80 807 


92 3S1 


07 619 88 425 







9 

log cos 


9 

log cot 


10 9 

log tan log sin 




t 


r 







40° 




47 


f 


log sin 


log tan 


log cot 


log cos 


t 




9 

80S07 


9 

92 3S1 


10 

07 619 


9 

SS425 







60 


1 


S0S22 


92 407 


07 593 


88 415 


59 


2 


SO 837 


92 433 


07 567 


SS404 


58 


3 


SO S52 


92 45S 


07 542 


88 394 


57 


4 


SO 867 


92 484 


07 516 


88 383 


56 


5 


S0 8S2 


92 510 


07 490 


8S372 


55 


6 


SO 897 


92 535 


07 465 


SS362 


54 


7 


80 912 


92 561 


07 439 


88 351 


53 


8 


80 927 


92 587 


07 413 


SS340 


52 


9 


80 942 


92 612 


07 388 


88 330 


51 


10 


80 957 


92 638 


07 362 


88 319 


50 


11 


80 972 


92 663 


07 337 


8S30S 


49 


12 


80 987 


92 689 


07 311 


88 298 


48 


13 


81002 


92 715 


07 285 


88 287 


47 


14 


81017 


92 740 


07 260 


88 276 


46 


15 


81032 


92 766 


07 234 


88 266 


45 


16 


81047 


92 792 


07 208 


88 255 


44 


17 


81061 


92 817 


07 183 


88 244 


43 


18 


81076 


92 843 


07 157 


88 234 


42 


19 


81091 


92 868 


07132 


88 223 


41 


20 


81106 


92S94 


07106 


88 212 


40 


21 


81121 


92 920 


07 080 


88 201 


39 


22 


81136 


92 945 


07 055 


88191 


38 


23 


81151 


92 971 


07 029 


88 180 


37 


24 


81166 


92 996 


07 004 


8S169 


36 


25 


81180 


93 022 


06 978 


8S158 


35 


26 


81195 


93 048 


06 952 


S8 14S 


34 


27 


81210 


93 073 


06 927 


SS137 


33 


28 


81225 


93 099 


06 901 


88 126 


32 


29 


81240 


93 124 


06 876 


88115 


31 


30 


81254 


93 150 


06 850 


88 105 


30 


31 


81269 


93 175 


06S25 


88 094 


29 


32 


81284 


93 201 


06 799 


88 083 


2S 


33 


81299 


93 227 


06 773 


88 072 


27 


34 


81314 


93 252 


06 748 


88 061 


26 


35 


81328 


93 278 


06 722 


88 051 


25 


36 


81343 


93 303 


06 697 


88 040 


24 


37 


81358 


93 329 


06 671 


8S029 


23 


38 


SI 372 


93 354 


06 646 


88 018 


22 


39 


81387 


93 380 


06 620 


88 007 


21 


40 


81402 


93 406 


06 594 


87 996 


20 


41 


81417 


93 431 


06 569 


87 985 


19 


42 


SI 431 


93 457 


06 543 


87 975 


18 


43 


81446 


93 482 


06 518 


87 964 


17 


44 


81461 


93 508 


06 492 


87 953 


16 


45 


81475 


93 533 


06 467 


87 942 


15 


46 


81490 


93 559 


06 441 


87 931 


14 


47 


81505 


93 584 


06 416 


87 920 


13 


48 


81519 


93 610 


06 390 


87 909 


12 


49 


81534 


93 636 


06 364 


S7S98 


11 


50 


81549 


93 661 


06 339 


87 887 


10 


51 


SI 563 


93 687 


06 313 


87 877 


9 


52 


81578 


93 712 


06 28S 


87S66 


8 


53 


81592 


93 738 


06 262 


S7 855 


7 


54 


81607 


93 763 


06 237 


S7 844 


6 


55 


81622 


93 7S9 


06 211 


87 833 


5 


56 


81636 


93S14 


06186 


87 822 


4 


57 


81651 


93 840 


06160 


87 811 


3 


58 


81665 


93 865 


06135 


S7S00 


2 


59 


81680 


93 891 


06109 


87 7S9 


1 


60 


81694 


93 916 


06 0S4 


87 778 







9 

log cos 


9 

log cot 


10 

log tan 


9 

log sin 




t 


t 



50 c 



49' 



48 




41° 






t 


log sin 


log tan 


log cot 


log cos 


t 




9 


9 


io 


9 




o 


81694 


93 916 


06 084 


87 778 


60 


1 


81709 


93 942 


06 05S 


S7 767 


59 


2 


81723 


93 967 


06 033 


87 756 


58 


3 


S173S 


93 993 


06 007 


87 745 


57 


4 


81752 


94 01S 


05 982 


S7 734 


56 


5 


81767 


94 044 


05 956 


87 723 


55 


6 


81781 


94 069 


05 931 


S7 712 


54 


7 


SI 796 


94 095 


05 905 


87 701 


53 


8 


81810 


94 120 


05 8SO 


87 690 


52 


9 


SI 825 


94146 


05 854 


87 679 


51 


10 


81S39 


94171 


05 829 


87 668 


50 


11 


81854 


94197 


05 803 


87 657 


49 


12 


S1S6S 


94 222 


05 778 


87 646 


48 


13 


81882 


94 248 


05 752 


87 635 


47 


14 


81S97 


94 273 


05 727 


87 624 


46 


15 


81911 


94 299 


05 701 


S7 613 


45 


16 


81 926 


94 324 


05 676 


87 601 


44 


17 


SI 940 


94 350 


05 650 


87 590 


43 


IS 


81955 


94 375 


05 625 


87 579 


42 


19 


81969 


94 401 


05 599 


87 568 


41 


20 


81983 


94 426 


05 574 


87 557 


40 


21 


81998 


94 452 


05 548 


87 546 


39 


22 


82 012 


94 477 


05 523 


S7 535 


38 


23 


S2 026 


94 503 


05 497 


S7 524 


37 


24 


82 041 


94 528 


05 472 


87 513 


36 


25 


S2 055 


94 554 


05 446 


87 501 


35 


26 


82 069 


94 579 


05 421 


87 490 


34 


27 


S2 0S4 


94 604 


05 396 


87 479 


33 


28 


82 098 


94 630 


05 370 


S7 46S 


32 


29 


82 112 


94 655 


05 345 


87 457 


31 


30 


82 126 


94 681 


05 319 


87 446 


30 


31 


82 141 


94 706 


05 294 


87 434 


29 


32 


S2 155 


94 732 


05 26S 


87 423 


28 


33 


82 169 


94 757 


05 243 


87 412 


27 


34 


82 184 


94 783 


05 217 


87 401 


26 


35 


82198 


94 808 


05 192 


87 390 


25 


36 


82 212 


94 834 


05 166 


87 378 


24 


37 


S2 226 


94 859 


05 141 


87 367 


23 


38 


S2 240 


94 884 


05 116 


87 356 


22 


39 


82 255 


94 910 


05 090 


87 345 


21 


40 


82 269 


94 935 


05 065 


87 334 


20 


41 


82 283 


94 961 


05 039 


87 322 


19 


42 


82 297 


94 986 


05 014 


87 311 


IS 


43 


82 311 


95 012 


04 988 


87 300 


17 


44 


82 326 


95 037 


04 963 


87 2SS 


16 


45 


82 340 


95 062 


04 938 


87 277 


15 


46 


S2 354 


95 OSS 


04 912 


87 266 


14 


47 


82 368 


95 113 


04 887 


87 255 


13 


48 


82 382 


95 139 


04 861 


87 243 


12 


49 


82 396 


95 164 


04S36 


87 232 


11 


50 


82 410 


95 190 


04 810 


87 221 


10 


51 


82 424 


95 215 


04 785 


87 209 


9 


52 


82 439 


95 240 


04 760 


S719S 


S 


53 


82 453 


95 266 


04 734 


87 1S7 


7 


54 


82 467 


95 291 


04 709 


87175 


6 


55 


82 481 


95 317 


04 683 


S7 164 


5 


56 


82 495 


95 342 


04 65S 


87 153 


4 


57 


82 509 


95 368 


04 632 


87 141 


3 


58 


82 523 


95 393 


04 607 


87 130 


2 


59 


82 537 


95 41S 


04 5S2 


87119 


1 


60 


82 551 


95 444 


04 556 


87107 







9 

log COS 


9 

log cot 


IO 

log tan 


9 

log sin 




t 


- t 



42 c 



t 


log sin 


log tan 


log cot 


log cos 


/ 




9 


9 


10 


9 







82 551 


95 444 


04 556 


87107 


60 


1 


82 565 


95 469 


04 531 


87 096 


59 


2 


82 579 


95 495 


04 505 


87 085 


58 


3 


82 593 


95 520 


04 480 


87 073 


57 


4 


S2 607 


95 545 


04 455 


87 062 


56 


5 


82 621 


95 571 


04 429 


87 050 


55 


6 


82 635 


95 596 


04 404 


87 039 


54 


7 


82 649 


95 622 


04 378 


87 02S 


53 


8 


82 663 


95 647 


04 353 


87 016 


52 


9 


82 677 


95 672 


04 328 


87 005 


51 


10 


82 691 


95 69S 


04 302 


S6 993 


50 


11 


82 705 


95 723 


04 277 


S6 9S2 


49 


12 


82 719 


95 748 


04 252 


86 970 


48 


13 


82 733 


95 774 


04 226 


86 959 


47 


14 


82 747 


95 799 


04 201 


S6 947 


46 


15 


82 761 


95 825 


04175 


S6 936 


45 


16 


82 775 


95 850 


04 150 


86 924 


44 


17 


82 7S8 


95 875 


04 125 


S6 913 


43 


18 


82 802 


95 901 


04 099 


86 902 


42 


19 


82 816 


95 926 


04 074 


S6S90 


41 


20 


82 830 


95 952 


04 048 


86 879 


40 


21 


S2 844 


95 977 


04 023 


S6S67 


39 


22 


82 858 


96 002 


03 998 


86 855 


3S 


23 


82 872 


96 02S 


03 972 


86 844 


37 


24 


82 885 


96 053 


03 947 


86 832 


36 


25 


82 899 


96 07S 


03 922 


86 821 


35 


26 


82 913 


96 104 


03 896 


86 809 


34 


27 


82 927 


96129 


03 871 


86 798 


33 


2S 


82 941 


96155 


03 845 


S6 7S6 


32 


29 


82^55 


96180 


03S20 


86 775 


31 


30 


82 968 


96'205 


03 795 


86 763 


30 


31 


82 982 


96 231 


03 769 


S6 752 


29 


32 


82 996 


96 256 


03 744 


S6 740 


28 


33 


83 010 


96 281 


03 719 


S6 72S 


27 


34 


83 023 


96 307 


03 693 


86 717 


26 


35 


83 037 


96 332 


03 668 


S6 705 


25 


36 


83 051 


96 357 


03 643 


86 694 


24 


37 


83 065 


96 383 


03 617 


S6 682 


23 


3S 


83 078 


96 40S 


03 592 


86 670 


22 


39 


83 092 


96 433 


03-567 


86 659 


21 


40 


83 106 


96 459 


03 541 


86 647 


20 


41 


83 120 


96 484 


03 516 


S6 635 


19 


42 


83 133 


96 510 


03 490 


86 624 


18 


43 


83 147 


96 535 


03 465 


S6 612 


17 


44 


83 161 


96 560 


03 440 


86 600 


16 


45 


83 174 


96 586 


03 414 


86 589 


15 


46 


83 188 


96 611 


03 389 


S6 577 


14 


47 


83 202 


96 636 


03 364 


86 565 


13 


48 


83 215 


96 662 


03 338 


86 554 


12 


49 


S3 229 


96 687 


03 313 


86 542 


11 


50 


83 242 


96 712 


03 2SS 


S6 530 


10 


51 


S3 256 


96 738 


03 262 


86 518 


9 


52 


83 270 


96 763 


03 237 


S6 507 


8 


53 


83 283 


96 78S 


03 212 


86 495 


7 


54 


83 297 


96S14 


03 186 


S6 4S3 


6 


55 


S3 310 


96 839 


03 161 


S6 472 


5 


56 


S3 324 • 


96 864 


03 136 


86 460 


4 


57 


S3 33S 


96 890 


03 110 


S6 448 


3 


5S 


S3 351 


96 915 


03 085 


86 436 


2 


59 


S3 365 


96 940 


03 060 


86 425 


1 


60 


83 37S 


96 966 


03 034 


86 413 








9 


9 


10 


9 






t 


log cos 


log cot 


log tan 


log sin 


t 



48 c 



47 c 



43 c 



t 


log sin 


log tan 


log cot 


log cos 


t 




9 

83 378 


9 

96 966 


10 

03 034 


9 

86 413 







60 


1 


83 392 


96 991 


03 009 


S6 401 


59 


2 


83 405 


97 016 


02 9S4 


86 3S9 


58 


3 


83 419 


97 042 


02 958 


86 377 


57 


4 


83 432 


97 067 


02 933 


86 366 


56 


5 


83 446 


97 092 


02 90S 


86 354 


55 


6 


83 459 


97 US 


02 882 


86 342 


54 


7 


83 473 


97 143 


02 857 


S6 330 


53 


S 


S3 4S6 


97 16S 


02 832 


86 31S 


52 


9 


83 500 


97193 


02 807 


86 306 


51 


10 


S3 513 


97 219 


02 781 


S6 295 


50 


11 


83 527 


97 244 


02 756 


S6 2S3 


49 


12 


S3 540 


97 269 


02 731 


86 271 


48 


13 


S3 554 


97 295 


02 705 


86 259 


47 


14 


83 567 


97 320 


02 680 


S6 247 


46 


15 


83 581 


97 345 


02 655 


86 235 


45 


16 


83 594 


97 371 


02 629 


86 223 


44 


17 


83 608 


97 396 


02 604 


86 211 


43 


18 


83 621 


97 421 


02 579 


86 200 


42 


19 


83 634 


97 447 


02 553 


861SS 


41 


20 


S3 648 


97 472 


02 52S 


86176 


40 


21 


83 661 


97 497 


02 503 


86 164 


39 


22 


83 674 


97 523 


02 477 


86 152 


38 


23 


S3 6SS 


97 54S 


02 452 


86140 


37 


24 


83 701 


97 573 


02 427 


86128 


36 


25 


S3 715 


97 598 


02 402 


86 116 


35 


26 


83 728 


97 624 


02 376 


86104 


34 


27 


83 741 


97 649 


02 351 


S6 092 


33 


28 


83 755 


97 674 


02 326 


S6 0S0 


32 


29 


83 768 


97 700 


02 300 


86 068 


31 


30 


83 781 


97 725 


02 275 


86 056 


30 


31 


S3 795 


97 750 


02 250 


86 044 


29 


32 


83 SOS 


97 776 


02 224 


86 032 


28 


33 


83 821 


97 801 


02 199 


86 020 


27 


34 


83 834 


97 826 


02 174 


S6 00S 


26 


35 


83S4S 


97 851 


02149 


85 996 


25 


36 


S3S61 


97 877 


02 123 


S5 984 


24 


37 


83 874 


97 902 


02 098 


85 972 


23 


38 


83 8S7 


97 927 


02 073 


85 960 


22 


39 


83 901 


97 953 


02 047 


S5 94S 


21 


40 


83 914 


97 978 


02 022 


85 936 


20 


41 


83 927 


98 003 


01997 


85 924 


19 


42 


83 940 


98 029 


01971 


S5 912 


IS 


43 


83 954 


9S054 


01946 


85 900 


17 


44 


83 967 


98 079 


01921 


S5 888 


16 


45 


83 9S0 


98 104 


01896 


85 876 


15 


46 


83 993 


98 130 


01S70 


85 864 


14 


47 


84 006 


98155 


01S45 


S5 851 


13 


48 


84 020 


98 180 


01820 


S5S39 


12 


49 


84 033 


98 206 


01794 


S5S27 


11 


50 


84 046 


98 231 


01769 


85S15 


10 


51 


S4 059 


98 256 


01744 


85 803 


9 


52 


84 072 


9S-2S1 


01719 


85 791 


8 


53 


S4 0S5 


98 307 


01693 


85 779 


7 


54 


84 098 


9S332 


0166S 


85 766 


6 


55 


84 112 


98 357 


01643 


85 754 


5 


56 


S4 125 


98 3S3 


01617 


85 742 


4 


57 


84 138 


9S40S 


01592 


85 730 


3 


5S 


84 151 


98 433 


01567 


S5 718 


2 


59 


S4 164 


98 458 


01542 


85 706 


1 


60 


84 177 


98 484 


01516 


85 693 







9 


9 


10 


9 


-H 


t 


log cos 


log cot 


log tan 


log sin 


' 







44° 




49 


t 


log sin 


log tan 


log cot 


log cos 


t 




9 

84 177 


9 

98 484 


10 

01516 


9 

85 693 







60 


1 


84 190 


98 509 


01491 


85 681 


59 


2 


84 203 


98 534 


01466 


85 669 


58 


3 


84 216 


98 560 


01440 


85 657 


57 


4 


84 229 


9S5S5 


01415 


85 645 


56 


5 


84 242 


98 610 


01390 


85 632 


55 


6 


84 255 


98 635 


01365 


85 620 


54 


7 


84 269 


9S661 


01339 


85 608 


53 


S 


S4 2S2 


98 6S6 


01314 


85 596 


52 


9 


84 295 


98 711 


01289 


85 583 


51 


10 


84 30S 


98 737 


01263 


85 571 


50 


11 


84 321 


98 762 


01238 


85 559 


49 


12 


84 334 


9S7S7 


01213 


85 547 


48 


13 


84 347 


9S812 


01188 


85 534 


47 


14 


84 360 


98 838 


01162 


85 522 


46 


15 


84 373 


98 863 


01137 


85 510 


45 


16 


84 385 


98SS8 


01112 


85 497 


44 


17 


84 398 


98 913 


01087 


85 485 


43 


18 


S4 411 


98 939 


01061 


85 473 


42 


19 


84 424 


98 964 


01036 


85 460 


41 


20 


84 437 


98 989 


01011 


S5 44S 


40 


21 


84 450 


99 015 


00 985 


85 436 


39 


22 


S4 463 


99 040 


00 960 


85 423 


38 


23 


84 476 


99 065 


00 935 


85 411 


37 


24 


84 489 


99 090 


00 910 


85 399 


36 


25 


84 502 


99116 


00 884 


85 386 


35 


26 


84 515 


99141 


00 859 


85 374 


34 


27 


84 528 


99 166 


00 834 


85 361 


33 


28 


84 540 


99191 


00 809 


85 349 


32 


29 


84 553 


99 217 


00 783 


85 337 


31 


30 


84 566 


99 242 


00 758 


85 324 


30 


31 


84 579 


99 267 


00 733 


85 312 


29 


32 


84 592 


99 293 


00 707 


85 299 


28 


33 


84 605 


99 318 


00 6S2 


85 2S7 


27 


34 


84 618 


99 343 


00 657 


85 274 


26 


35 


84 630 


99 368 


00 632 


85 262 


25 


36 


S4 643 


99 394 


00 606 


85 250 


24 


37 


84 656 


99 419 


00 581 


85 237 


23 


3S 


84 669 


99 444 


00 556 


85 225 


22 


39 


84 6S2 


99 469 


00 531 


85 212 


21 


40 


84 694 


99 495 


00 505 


85 200 


20 


41 


S4 707 


99 520 


00 480 


85 187 


19 


42 


84 720 


99 545 


00 455 


85 175 


18 


43 


84 733 


99 570 


00 430 


85 162 


17 


44 


84 745 


99 596 


00 404 


85 150 


16 


45 


84 758 


99 621 


00 379 


85 137 


15 


46 


84 771 


99 646 


00 354 


85 125 


14 


47 


84 784 


99 672 


00 328 


85 112 


13 


48 


84 796 


99 697 


00 303 


85 100 


12 


49 


84 809 


99 722 


00 278 


85 087 


11 


50 


84 822 


99 747 


00 253 


85 074 


10 


51 


84 835 


99 773 


00 227 


85 062 


9 


52 


84 847 


99 798 


00 202 


85 049 


8 


53 


84S60 


99 823 


00 177 


85 037 


7 


54 


84S73 


99 848 


00152 


85 024 


6 


55 


84 885 


99 874 


00 126 


85 012 


5 


56 


84S9S 


99 899 


00101 


84 999 


4 


57 


84 911 


99 924 


00 076 


84 986 


3 


58 


84 923 


99 949 


00 051 


S4 974 


2 


59 


S4 936 


99 975 


00 025 


84 961 


1 


60 


84 949 


00 000 


00 000 


84 949 


O 





9 


10 


10 


9 




t 


log cos 


log cot 


log tan 


log sin 


t 



46 : 



45 



50 










TABLE IV. 


HAN CAN BE DONE BY 


For Determining wite 


[ Greater Accuracy i 


means of Table III. : 




1. log sin, log tan, and log cot, when the angle is between 0° and 2° ; 


2. log cos, log tan, and log cot, when the angle is between 88° and 90° ; 


3. The value of the angle when the logarithm of the function does not 


lie between the limits 8. 54 684 and 11. 45 316. 




FORMULAS FOR THE USE OF THE 1STUMBERS S AND T. 


I. When the angle a is between 0° and 2° : 




log sin a = log a" + S. 


log a" = log sin a — S, 




log tan a = log a" + T. 


= log tan a — T, 




log cot a = colog tan a. 


= colog cot a — T. 




II. When the angle a is between 88° and 90° : 




log cos a = log (90° - a)" + S. 


log (90° - a)" = log cos a - 


-s, 


log cot a = log (90° - a)" + T. 


= log cot a - 


- T, 


log tan a = colog cot a. 


= colog tan 


a — T, 


. * and a = 90° - (90 


>-«). 


»«VKo« 




Values of S ato T, . 




a" S log sin a 




a" T log tan a 


a T 


log tan a 


— 




— 


5146 


8. 39 713 


4. 68 557 




4. 68 557 


4. 68 567 




2 409 8. 06 740 




200 6. 98 660 


5 424 


8. 41 999 


4. 68 556 




4. 68 558 


4. 68 568 




3 417 8. 21 920 




1 726 7. 92 263 


5 689 


8. 44 072 


4. 68 555 




4. 68 559 


4. 68 569 




3 823 8. 26 795 




2 432 8. 07 156 


5 941 


8. 45 955 


4. 68 555 




4. 68 560 


4. 68 570 




4 190 8. 30 776 




2 976 8. 15 924 


6184 


8. 47 697 


4. 68 554 




• 4.68 561 


4. 68 571 




4 840 8. 37 038 




3 434 8. 22 142 


6 417 


8. 49 305 


4. 68 553 




4. 68 562 


4. 68 572 




5 414 8. 4.1 904 




3 838 . 8. 26 973 


6 642 


S. 50 802 


4. 68 552 




4. 68 563 


4. 68 573 




5 932 8.45 872 




4 204 8. 30 930 


6 859 


8. 52 200 


4. 68 551 




4. 68 564 


4. 68 574 




6 408 8. 49 223 




4 540 8.34 270 


7 070 


8.53 516 


4. 6S 550 




4. 68 565 


4. 68 575 




6 633 8. 50 721 




4 699 8. 35 766 


7173 


S. 54 145 


4. 68 550 




4. 68 565 


4. 68 575 




6 851 8.52 125 




4 853 8. 37 167 


7 274 


S. 54 753 


4. 68 549 




4. 68 566 






7 267 8. 54 684 




5 146 8. 39 713 






a" S log sin a 




a" . T log tan a 


a T 


log tan a 1 



TABLE V.— Circumferences and Areas of Circles. 61 







If .ZV"= the radius of the circle, the circumference = 2 ?r 


n: 








If JST = the 


radius of the circle, the < 


irea 


= TriV 2 . 








If iV = the circumference of the circle, the radius = — 

2tt 


N. 








If iV" = the circumference of the circle, the area = — 

4tt 


2V 2 . 




N 


2TT2? 


Wjf2 


2ir 


if 

0.00 


N 


27TJV 


irJT* 


±jst 

2ir 


47T 





0.00 


0.0 


0.000 


50 


314. 16 


7 854 


7.96 


198. 94 


1 


6.28 


3.1 


0.159 


0.08 


51 


320. 44 


8171 


8.12 


206. 98 


2 


12.57 


12.6 


0.318 


0.32 


52 


326. 73 


8 495 


8.2S 


215. 18 


3 


18.85 


28.3 


0.477 


0.72 


53 


333. 01 


8 825 


8.44 


223. 53 


4 


25. 13 


50.3 


0.637 


1.27 


54 


339. 29 


9161 


8.59 


232. 05 


5 


31.42 


78.5 


0.796 


1.99 


55 


345. 58 


9 503 


8.75 


240. 72 


6 


37.70 


113.1 


0.955 


2.86 


56 


351.86 


9 852 


8.91 


249. 55 


7 


43.98 


153.9 


1.114 


3.90 


57 


358. 14 


10 207 


9.07 


258. 55 


8 


50.27 


201.1 


1.273 


5.09 


58 


364. 42 


10 568 


9.23 


267. 70 


9 


56.55 


254.5 


1.432 


6.45 


59 


370. 71 


10 936 


9.39 


277. 01 


10 


62.83 


.314.2 


1.592 


7.96 


60 


376. 99 


11310 


9.55 


286. 48 


11 


69.12 


380.1 


1.751 


9.63 


61 


383. 27 


11690 


9.71 


296. 11 


12 


75.40 


452.4 


1.910 


11.46 


62 


389. 56 


12 076 


9.87 


305. 90 


13 


81. 6S 


530.9 


2.069 


13.45 


63 


395. 84 


12 469 


10.03 


315. 84 


14 


87.96 


615.8 


2.228 


15.60 


64 


402. 12 


12 868 


10.19 


325. 95 


15 


94.25 


706.9 


2.387 


17.90 


65 


408. 41 


13 273 


10.35 


336. 21 


16 


100. 53 


80+. 2 


2.5+6 


20.37 


66 


414. 69 


13 685 


10.50 


346. 64 


17 


106. 81 


907.9 


2.706 


23.00 


67 


420. 97 


14103 


10.66 


357. 22 


IS 


113. 10 


1017.9 


2.865 


25.78 


68 


427. 26 


14 527 


10.82 


367. 97 


19 


119. 38 


1 134. 1 


3.02+ 


28. 73 


69 


433. 54 


14 957 


10.98 


378. 87 


20 


125. 66 


1 256. 6 


3.183 


31.83 


70 


439. S2 


15 394 


11.14 


389. 93 


21 


131.95 


1 385. 4 


3.3+2 


35. 09 


71 


446. 11 


15 837 


11.30 


401. 15 


22 


138. 23 


1 520. 5 


3.501 


38.52 


72 


452. 39 


16 286 


11.46 


412. 53 


23 


144. 51 


1661.9 


3.661 


42.10 


73 


458. 67 


16 742 


11.62 


424. 07 


24 


150. 80 


1 S09. 6 


3.820 


45.8+ 


74 


464. 96 


17 203 


11.78 


435. 77 


25 


157. OS 


1 963. 5 


3.979 


49.74 


75 


471. 24 


17 671 


11.94 


447. 62 


26 


163. 36 


2 123. 7 


+. 13S 


53.79 


76 


477. 52 


18146 


12.10 


459. 64 


27 


169. 65 


2 290. 2 


4.297 


58.01 


77 


483. 81 


18 627 


12.25 


471. 81 


28 


175.93 


2 463. 


4.456 


62.39 


78 


490. 09 


19113 


12.41 


484. 15 


29 


182. 21 


2 6+2. 1 


4.615 


66.92 


79 


496. 37 


19 607 


12.57 


496. 64 . 


30 


18S. 50 


2 827. 4 


4.775 


71.62 


80 


502. 65 


20106 


12.73 


509. 30 


31 


19+. 78 


3 019. 1 


4.934 


76.47 


81 


508. 94 


20 612 


12.89 


522. 11 


32 


201. 06 


3 217.0 


5.093 


81.49 


82 


515. 22 


21124 


13.05 


535. 08 


33 


207. 35 


3 421. 2 


5.252 


86.66 


83 


521. 50 


21642 


13.21 


548. 21 


34 


213. 63 


3 631. 7 


5.411 


91.99 


84 


527. 79 


22167 


13.37 


561. 50 


35 


219. 91 


3 84S. 5 


5.570 


97.48 


85 


534. 07 


22 698 


13.53 


574. 95 


36 


226. 19 


4 071.5 


5.730 


103. 13 


86 


540. 35 


23 235 


13.69 


588. 55 


37 


232. 48 


4 300. 8 


5.8S9 


108. 94 


87 


546. 64 


23 779 


13.85 


602. 32 


3S 


23S. 76 


4 536. 5 


6.048 


114.91 


88 


552.92 


24 328 


14.01 


616. 25 


39 


245. 04 


4 778.4 


6.207 


121. 04 


89 


559. 20 


24 885 


14.16 


630. 33 


40 


251.33 


5 026. 5 


6.366 


127. 32 


90 


565. 49 


25 447 


14.32 


644. 58 


41 


257. 61 


5 281.0 


6.525 


133. 77 


91 


571.77 


26 016 


14.48 


658. 98 


42 


263. 89 


5-541.8 


6. 6S5 


1+0. 37 


92 


578. 05 


26 590 


14.64 


673. 54 


43 


270. 18 


5 SOS. 8 


6.8++ 


147. 14 


93 


584. 34 


27 172 


14.80 


688. 27 


44 


276. 46 


6 0S2. 1 


7.003 


154. 06 


9+ 


590. 62 


27 759 


14.96 


703. 15 


45 


2S2. 74 


6 361.7 


7.162 


161. 14 


95 


596. 90 


28 353 


15.12 


718. 19 


46 


289 03 


6 647. 6 


7.321 


168. 39 


96 


603. 19 


28 953 


15.28 


733. 39 


47 


295.31 


6 939. 8 


7. 4S0 


175. 79 


97 


609. 47 


29 559 


15.44 


748. 74 


4S 


301. 59 


7 238. 2 


7.639 


183.35 


98 


615. 75 


30 172 


15.60 


764. 26 


49 


307. SS 


7 543. 


7.799 


191. 07 


99 


622. 04 


30 791 


15.76 


779. 94 


50 


314. 16 


7 854. 


7.958 


198. 94 


100 


628. 32 


31416 


15.92 


795. 77 


N 


2 7TiV 


irN 2 


l-N 


JL^a 


N 


2ir_iV 


±-V 


±-N* 








<2,ir 


4ir 








lit 


47T 



52 


TABLE VI. -NATUBAL FUNCTIONS 


• 




/ 


o° 


1° 


-2° 


3° 


4° 


f 




sin 


cos 


sin cos 


sin cos 


sin 


cos 


sin 


cos 




o 


0000 


1.000 


0175 9998 


0349 9994 


0523 


9986 


0698 


9976 


60 


i 


0003 


1.000 


0177 9998 


0352 9994 


0526 


9986 


0700 


9975 


59 


2 


0006 


1.000 


0180 9998 


0355 9994 


0529 


9986 


0703 


9975 


58 


3 


0009 


1.000 


0183 9998 


0358 9994 


0532 


9986 


0706 


9975 


57 


' 4 


0012 


1.000 


0186 9998 


0361 9993 


0535 


9986 


0709 


9975 


56 


5 


0015 


1.000 


0189 9998 


0364 9993 


0538 


9986 


0712 


9975 


55 


6 


0017 


1.000 


0192 9998 


0366 9993 


0541 


9985 


0715 


9974 


54 


7 


0020 


1.000 


0195 9998 


0369 9993 


0544 


9985 


0718 


9974 


53 


8 


0023 


1.000 


0198 9998 


0372 9993 


0547 


9985 


0721 


9974 


52 


9 


0026 


1.000 


0201 9998 


0375 9993 


0550 


9985 


0724 


9974 


51 


10 


0029 


1.000 


0204 9998 


0378 9993 


0552 


9985 


0727 


9974 


50 


11 


0032 


1.000 


0207 9998 


0381 9993 


0555 


9985 


0729 


9973 


49 


12 


0035 


1.000 


0209 9998 


0384 9993 


0558 


9984 


0732 


9973 


48 


13 


0038 


1.000 


0212 9998 


0387 9993 


0561 


9984 


0735 


9973 


47 


14 


0041 


1.000 


0215 9998 


0390 9992 


0564 


9984 


0738 


9973 


46 


15 


0044 


1.000 


0218 9998 


0393 9992 


0567 


9984 


0741 


9973 


45 


16 


0047 


1.000 


0221 9998 


0396 9992 


0570 


9984 


0744 


9972 


44 


17 


0049 


1.000 


0224 9997 


0398 9992 


0573 


9984 


0747 


9972 


43 


IS 


0052 


1.000 


0227 9997 


0401 9992 


0576 


9983 


0750 


9972 


42 


19 


0055 


1.000 


0230 9997 


0404 9992 


0579 


9983 


0753 


9972 


41 


20 


0058 


1.000 


0233 9997 


0407 9992 


0581 


9983 


0756 


9971 


40 


21 


0061 


1.000 


0236 9997 


0410 9992 


0584 


9983 


0758 


9971 


39 


22 


0064 


1.000 


0239 9997 


0413 9991 


0587 


9983 


0761 


9971 


38 


23 


0067 


1.000 


0241 9997 


0416 9991 


0590 


9983 


0764 


9971 


37 


24 


0070 


1.000 


0244 9997 


0419 9991 


0593 


9982 


0767 


9971 


36 


25 


0073 


1.000 


0247 9997 


0422 9991 


0596 


9982 


0770 


9970 


35 


26 


0076 


1.000 


0250 9997 


0425 9991 


0599 


9982 


0773 


9970 


34 


27 


0079 


1.000 


0253 9997 


0427 9991 


0602 


9982 


0776 


9970 


33 


2S 


0081 


1.000 


0256 9997 


0430 9991 


0605 


9982 


0779 


9970 


32 


29 


0084 


1.000 


0259 9997 


0433 9991 


.0608 


9982 


0782 


9969 


31 


30 


0087 


1.000 


0262 9997 


0436 9990 


0610 


9981 


0785 


9969 


30 


31 


0090 


1.000 


0265 9996 


0439 9990 


0613 


9981 


0787 


9969 


29 


32 


0093 


1.000 


0268 9996 


0442 9990 


0616 


9981 


0790 


9969 


28 


33 


0096 


1000 


0270 9996 


0445 9990 


0619 


9981 


0793 


9968 


27 


34 


0099 


1.000 


0273 9996 


0448 9990 


0622 


9981 


0796 


9968 


26 


35 


0102 


9999 


0276 9996 


0451 9990 


0625 


9980 


0799 


9968 


25 


36 


0105 


9999 


0279 9996 


0454 9990 


0628 


9980 


0802 


9968 


24 


37 


0108 


9999 


0282 9996 


0457 9990 


0631 


9980 


0805 


9968 


23 


38 


0111 


9999 


0285 9996 


0459 9989 


0634 


9980 


0808 


9967 


22 


39 


0113 


9999 


02SS 9996 


0462 9989 


0637 


9980 


0811 


9967 


21 


40 


0116 


9999 


0291 9996 


0465 9989 


0640 


9980 


0814 


9967 


20 


41 


0119 


9999 


0294 9996 


0468 9989 


0642 


9979 


0816 


9967 


19 


42 


0122 


9999 


0297 9996 


0471 9989 


0645 


9979 


0819 


9966 


IS 


43 


0125 


9999 


0300 9996 


0474 9989 


0648 


9979 


0822 


9966 


17 


44 


0128 


9999 


0302 9995 


0477 9989 


0651 


9979 


0825 


9966 


16 


45 


0131 


9999 


0305 9995 


0480 9988 


0654 


9979 


082S 


9966 


15 


46 


0134 


9999 


0308 9995 


0483 9988 


0657 


9978 


0831 


9965 


14 


47 


0137 


9999 


0311 9995 


■ 0486 9988 


0660 


9978 


0834 


9965 


13 


48 


0140 


9999 


0314 9995 


0488 9988 


0663 


9978 


0837 


9965 


12 


49 


0143 


9999 


0317 9995 


0491 9988 


0666 


9978 


0840 


9965 


11 


50 


0145 


9999 


0320 9995 


0494 9988 


0669 


9978 


0843 


9964 


10 


51 


0148 


9999 


0323 9995 


0497 9988 


0671 


9977 


0845 


9964 


9 


52 


0151 


9999 


0326 9995 


0500 9987 


0674 


9977 


0848 


9964 


8 


53 


0154 


9999 


0329 9995 


0503 9987 


0677 


9977 


0851 


9964 


7 


54 


0157 


9999 


0332 9995 


0506 9987 


06S0 


9977 


0854 


9963 


6 


55 


0160 


9999 


0334 9994 


0509 9987 


0683 


9977 


0857 


9963 


5 


56 


0163 


9999 


0337 9994 


0512 9987 


06S6 


9976 


0860 


9963 


4 


57 


0166 


9999 


0340 9994 


0515 9987 


0689 


9976 


0863 


9963 


3 


58 


0169 


9999 


0343 9994 


0518 99S7 


0692 


9976 


0866 


9962 


2 


59 


0172 


9999 


0346 9994 


0520 9986 


0695 


9976 


0S69 


9962 


1 


60 


0175 


9999 


0349 9994 


0523 9986 


069S 


9976 


0872 


9962 


O 




cos 


sin 


cos sin 


cos sin 


cos 


sin 


cos 


sin 




r 


89° 


88° 


87° 


80° 


85° 


t 



NATUKAL SINES AND COSINES. 



53 



/ 


5° 


6° 


7° 


8° 


9° 


t 




sin 


cos 


sin 


cos 


sin cos 


sin 


cos 


sin 


cos 


o 


0872 


9962 


1045 


9945 


1219 9925 


1392 


9903 


1564 


9877 


60 


1 


0874 


9962 


1048 


9945 


1222 9925 


1395 


9902 


1567 


9876 


59 


2 


0877 


9961 


1051 


9945 


1224 9925 


1397 


9902 


1570 


9876 


58 


3 


0S80 


9961 


1054 


9944 


1227 9924 


1400 


9901 


1573 


9876 


57 


4 


0SS3 


9961 


1057 


9944 


1230 9924 


1403 


9901 


1576 


9875 


56 


5 


0SS6 


9961 


1060 


9944 


1233 9924 


1406 


9901 


1579 


9875 


55 


6 


0889 


9960 


1063 


9943 


1236 9923 


1409 


9900 


1582 


9874 


54 


7 


0892 


9960 


1066 


9943 


1239 9923 


1412 


9900 


1584 


9874 


53 


8 


0S95 


9960 


1068 


9943 


1241 9923 


1415 


9899 


1587 


9873 


52 


9 


089S 


9960 


1071 


9942 


1245 9922 


1418 


9899 


1590 


9873 


51 


10 


0901 


9959 


1074 


9942 


1248 9922 


1421 


9899 


1593 


9872 


50 


11 


0903 


9959 


1077 


9942 


1250 9922 


1423 


9898 


1596 


9872 


49 


12 


0906 


9959 


1080 


9942 


1253 9921 


1426 


9898 


1599 


9871 


48 


13 


0909 


9959 


1083 


9941 


1256 9921 


1429 


9897 


1602 


9871 


47 


14 


0912 


9958 


1086 


9941 


1259 9920 


1432 


9897 


1605 


9870 


46 


15 


0915 


9958 


1089 


9941 


1262 9920 


1435 


9897 


1607 


9870 


45 


16 


0918 


9958 


1092 


9940 


1265 9920 


1438 


9896 


1610 


9869 


44 


17 


0921 


9958 


1094 


9940 


1268 9919 


1441 


9896 


1613 


9869 


43 


18 


0924 


9957 


1097 


9940 


1271 9919 


1444 


9895 


1616 


9869 


42 


19 


0927 


9957 


1100 


9939 


1274 9919 


1446 


9895 


1619 


9868 


41 


20 


0929 


9957 


1103 


9939 


1276 9918 


1449 


9894 


1622 


9868 


40 


21 


0932 


9956 


1106 


9939 


1279 9918 


1452 


9894 


1625 


9867 


39 


22 


0935 


9956 


1109 


9938 


12S2 9917 


1455 


9894 


1628 


9S67 


38 


23 


0938 


9956 


1112 


9938 


1285 9917 


1458 


9893 


1630 


9866 


37 


24 


0941 


9956 


1115 


9938 


1288 9917 


1461 


9893 


1633 


9866 


36 


25 


0944 


9955 


1118 


9937 


1291 9916 


1464 


9892 


1636 


9865 


35 


26 


0947 


9955 


1120 


9937 


1294 9916 


1467 


9892 


1639 


9865 


34 


27 


0950 


9955 


1123 


9937 


1297 9916 


1469 


9891 


1642 


9864 


33 


28 


0953 


9955 


1126 


9936 


1299 9915 


1472 


9891 


1645 


9864 


32 


29 


0956 


9954 


1129 


9936 


1302 9915 


1475 


9891 


1648 


9863 


31 


30 


0958 


9954 


1132 


9936 


1305 9914 


1478 


9890 


1650 


9863 


30 


31 


0961 


9954 


1135 


9935 


1308 9914 


1481 


9890 


1653 


9862 


29 


32 


0964 


9953 


1138 


9935 


1311 9914 


1484 


9889 


1656 


9862 


28 


33 


0967 


9953 


1141 


9935 


1314 9913 


1487 


9889 


1659 


9861 


27 


34 


0970 


9953 


1144 


9934 


1317 9913 


1490 


9888 


1662 


9861 


26 


35 


■ 0973 


9953 


1146 


9934 


1320 9913 


1492 


9888 


1665 


9860 


25 


36 


0976 


9952 


1149 


9934 


1323 9912 


1495 


9888 


1668 


9860 


24 


37 


0979 


9952 


1152 


9933 


1325 9912 


1498 


9887 


1671 


9859 


23 


38 


0982 


9952 


1155 


9933 


1328 9911 


1501 


98S7 


1673 


9S59 


22 


39 


0985 


9951 


1158 


9933 


1331 9911 


1504 


9886 


1676 


9859 


21 


40 


09S7 


9951 


1161 


9932 


1334 9911 


1507 


9886 


1679 


9858 


20 


41 


0990 


9951 


1164 


9932 


1337 9910 


1510 


9885 


1682 


9858 


19 


42 


0993 


9951 


1167 


9932 


1340 9910 


1513 


9885 


1685 


9S57 


IS 


43 


0996 


9950 


1170 


9931 


1343 9909 


1515 


9884 


16S8 


9857 


17 


44 


0999 


9950 


1172 


9931 


1346 9909 


1518 


9884 


1691 


9856 


16 


45 


1002 


9950 


1175 


9931 


1349 9909 


1521 


9884 


1693 


9856 


15 


46 


1005 


9949 


1178 


9930 


1351 9908 


1524 


9883 


1696 


9855 


14 


47 


1008 


9949 


1181 


9930 


1354 990S 


1527 


9883 


1699 


9S55 


13 


4S 


1011 


9949 


1184 


9930 


1357 9907 


1530 


9882 


1702 


9854 


12 


49 


1013 


9949 


1187 


9929 


1360 9907 


1533 


9882 


1705 


9854 


11 


50 


1016 


9948 


1190 


9929 


1363 9907 


1536 


9881 


1708 


9853 


10 


51 


1019 


9948 


1193 


9929 


1366 9906 


1538 


9881 


1711 


9853 


9 


52 


1022 


9948 


1196 


9928 


1369 9906 


1541 


9880 


1714 


9852 


8 


53 


1025 


9947 


1198 


992S 


1372 9905 


1544 


9880 


1716 


9S52 


7 


54 


1028 


9947 


1201 


9928 


1374 9905 


1547 


9880 


1719 


9851 


6 


55 


1031 


9947 


1204 


9927 


1377 9905 


1550 


9879 


1722 


9851 


5 


56 


1034 


9946 


1207 


9927 


13S0 9904 


1553 


9879 


1725 


9850 


4 


57 


1037 


9946 


1210 


9927 


1383 9904 


1556 


9878 


1728 


9850 


3 


58 


1039 


9946 


1213 


9926 


13S6 9903 


1559 


9878 


1731 


9849 


2 


59 


1042 


9946 


1216 


9926 


1389 9903 


1561 


9877 


1734 


9849 


1 


60 


1045 


9945 


1219 


9925 


1392 9903 


1564 


9877 


1736 


9848 







cos 


sin 


cos 


sin 


cos sin 


cos 


sin 


cos 


sin 




t 


84° 


83° 


82° 


81° 


80° 


t 



54 



NATITKAL SINES AND COSINES. 



/ 


10° 


11° 


12° 


13° 


14° 


t 




sin 


cos 


sin 


cos 


sin cos 


sin cos 


sin cos 







1736 


9848 


1908 


9816 


2079 9781 


2250 9744 


2419 9703 


60 


1 


1739 


9848 


1911 


9816 


2082 97S1 


2252 9743 


2422 9702 


59 


2 


1742 


9847 


1914 


9815 


2085 9780 


2255 9742 


2425 9702 


58 


3 


1745 


9847 


1917 


9815 


2088 9780 


2258 9742 


2428 9701 


57 


' 4 


1748 


9846 


1920 


9814 


2090 9779 


2261 9741 


2431 9700 


56 


5 


1751 


9846 


1922 


9813 


2093 9778 


2264 9740 


2433 9699 


55 


6 


1754 


9845 


1925 


9813 


2096 9778 


2267 9740 


2436 9699 


54 


7 


1757 


9845 


1928 


9S12 


2099 9777 


2269 9739 


2439 9698 


53 


8 


1759 


9844 


1931 


9812 


2102 9777 


2272 9738 


2442 9697 


52 


9 


1762 


9843 


1934 


9811 


2105 9776 


2275 9738 


2445 9697 


51 


10 


1765 


9843 


1937 


9811 


2108 9775 


2278 9737 


2447 9696 


50 


11 


1768 


9842 


1939 


9810 


2110 9775 


2281 9736 


2450 9695 


49 


12 


1771 


9842 


1942 


9810 


2113 9774 


2284 9736 


2453 9694 


48 


13 


1774 


9841 


1945 


9809 


2116 9774 


2286 9735 


2456 9694 


47 


14 


1777 


9841 


1948 


9808 


2119 9773 


2289 9734 


2459 9693 


46 


15 


1779 


9840 


1951 


9808 


2122 9772 


2292 9734 


2462 9692 


45 


16 


. 1782 


9840 


1954 


9807 


2125 9772 


2295 9733 


2464 9692 


44 


17 


1785 


9839 


1957 


9807 


2127 9771 


2298 9732 


2467 9691 


43 


18 


1788 


9839 


1959 


9806 


2130 9770 


2300 9732 


2470 9690 


42 


19 


1791 


983S 


1962 


9806 


2133 9770 


2303 9731 


2473 9689 


41 


20 


1794 


9838 


1965 


9805 


2136 9769 


2306 9730 


2476 9689 


40 


21 


1797 


9837 


1968 


9804 


2139 9769 


2309 9730 


2478 96SS 


39 


22 


1799 


9S37 


1971 


9804 


2142 9768 


2312 9729 


2481 9687 


38 


23 


1802 


9836 


1974 


9803 


2145 9767 


2315 9728 


2484 9687 


37 


24 


1805 


9836 


1977 


9S03 


2147 9767 


2317 9728 


2487 9686 


36 


25 


1808 


9835 


1979 


9802 


2150 9766 


2320 9727 


2490 9685 


35 


26 


1811 


9835 


1982 


9802 


2153 9765 


2323 9726 


2493 9684 


34 


27 


1814 


9834 


1985 


9801 


2156 9765 


2326 9726 


2495 9684 


33 


28 


1817 


9834 


1988 


9800 


2159 9764 


2329 9725 


2498 9683 


32 


29 


1819 


9833 


1991 


9800 


2162 9764 


2232 9724 


2501 9682 


31 


30 


1822 


9833 


1994 


9799 


2164 9763 


2334 9724 


2504 9681 


30 


31 


1825 


9S32 


1997 


9799 


2167 9762 


2337 9723 


2507 9681 


29 


32 


182S 


9831 


1999 


9798 


2170 9762 


2340 9722 


■2509 9680 


28 


33 


1831 


9831 


2002 


9798 


2173 9761 


2343 9722 


2512 9679 


27 


34 


1834 


9830 


2005 


9797 


2176 9760 


2346 9721 


2515 9679 


26 


35 


1837 


9830 


200S 


9796 


2179 9760 


2349 9720 


2518 9678 


25 


36 


1840 


9829 


2011 


9796 


2181 9759 


2351 9720 


2521 9677 


24 


37 


1842 


9829 


2014 


9795 


2184 9759 


2354 9719 


2524 9676 


- 23 


38 


1845 


9828 


2016 


9795 


2187 9758 


2357 9718 


2526 9676 


22 


39 


1848 


9828 


2019 


9794 


2190 9757 


2360 9718 


2529 9675 


21 


40 


1851 


9827 


2022 


9793 


2193 9"757 


2363 9717 


2532 9674 


20 


41 


1854 


9827 


2025 


9793 


2196 9756 


2366 9716 


2535 9673 


19 


42 


1857 


9826 


2028 


9792 


2198 9755 


2368 9715 


2538 9673 


IS 


43 


1860 


9826' 


2031 


9792 


2201 9755 


2371 9715 


2540 9672 


17 


44 


1862 


9825 


2034 


9791 


2204 9754 


2374 9714 


2543 9671 


16 


45 


1865 


9825 


2036 


9790 


2207 9753 


2377 9713 


2546 9670 


15 


46 


1S68 


9824 


2039 


9790 


2210 9753 


2380 9713 


2549 9670 


14 


47 


1871 


9823 


2042 


9789 


• 2213 9752 


2383 9712 


2552 9669 


13 


48 


1874 


9823 


2045 


9789 


2215 9751 


2385 9711 


2554 966S 


12 


49 


1877 


9822 


2048 


9788 


2218 9751 


2388 9711 


2557 9667 


11 


50 


1880 


9822 


2051 


9787 


2221 9750 


2391 9710 


2560 9667 


10 


51 


1882 


9821 


2054 


9787 


2224 9750 


2394 9709 


2563 9666 


9 


52 


1885 


9821 


2056 


9786 


2227 9749 


2397 9709 


2566 9665 


8 


53 


1888 


9820 


2059 


9786 


2230 9748 


2399 9708 


2569 9665 


7 


54 


1891 


9820 


2062 


9785 


2233 9748 


2402 9707 


2571 9664 


6 


55 


1894 


9819 


2065 


9784 


2235 9747 


2405 9706 


2574 9663 


5 


56 


1897 


9S18 


206S 


9784 


2238 9746 


2408 9706 


2577 9662 


4 


57 


1900 


9818 


2071 


9783 


2241 9746 


2411 9705 


2580 9662 


3 


5S 


1902 


9S17 


2073 


9783 


2244 9745 


2414 9704 


2583 9661 


2 


59 


1905 


9S17 


2076 


9782 


2247 9744 


2416 9704 


25S5 9660 


1 


60 


1908 


9816 


2079 


9781 


2250 9744 


2419 9703 


2588 9659 







cos 


sin 


cos 


sin 


cos sin 


cos sin 


cos sin 




t 


79° 


78° 


77° 


76° 


75° 


' | 



NATURAL SINES AND COSINES. 



55 



/ 


15° 


16° 


17° 


18° 


19° 


t 




sin 


cos 


sin 


cos 


sin 


cos 


sin 


cos 


sin 


cos 







25S8 


9659 


2756 


9613 


2924 


9563 


3090 


9511 


3256 


9455 


60 


1 


2591 


9659 


2759 


9612 


2926 


9562 


3093 


9510 


3258 


9454 


59 


2 


2594 


965S 


2762 


9611 


2929 


9561 


3096 


9509 


3261 


9453 


58 


3 


2597 


9657 


2165 


9610 


2932 


9560 


3098 


9508 


3264 


9452 


57 


4 


2599 


9656 


276S 


9609 


2935 


9560 


3101 


9507 


3267 


9451 


56 


5 


2602 


9655 


2770 


9609 


2938 


9S59 


3104 


9506 


3269 


9450 


55 


6 


2605 


9655 


2773 


9608 


2940 


9558 


3107 


9505 


3272 


9449 


54 


7 


260S 


9654 


2776 


9607 


2943 


9557 


3110 


9504 


3275 


9449 


53 


8 


2611 


9653 


2779 


9606 


2946 


9556 


3112 


9503 


3278 


9448 


52 


9 


' 2613 


9652 


2782 


9605 


2949 


9555 


3115 


9502 


3280 


9447 


51 


10 


2616 


9652 


2784 


9605 


2952 


9555 


3118 


9502 


3283 


9446 


50 


11 


2619 


9651 


27S7 


9604 


2954 


9554 


3121 


9501 


3286 


9445 


49 


12 


2622 


9650 


2790 


9603 


2957 


9553 


3123 


9500 


3289 


9444 


48 


13 


2625 


9649 


2793 


9602 


2960 


9552 


3126 


9499 


3291 


9443 


47 


14 


262S 


9649 


2795 


9601 


2963 


9551 


3129 


9498 


3294 


9442 


46 


15 


2630 


964S 


2798 


9600 


2965 


9550 


3132 


9497 


3297 


9441 


45 


16 


2633 


9647 


2801 


9600 


296S 


9549 


3134 


9496 


3300 


9440 


44 


17 


2636 


9646 


2S04 


9599 


2971 


9548 


3137 


9495 


3302 


9439 


43 


IS 


2639 


9646 


2807 


9598 


2974 


9548 


3140 


9494 


3305 


9438 


42 


19 


2642 


9645 


2S09 


9597 


2977 


9547 


3143 


9493 


3308 


9437 


41 


20 


2644 


9644 


2812 


9596 


2979 


9546 


3145 


9492 


3311 


9436 


40 


21 


2647 


9643 


2815 


9596 


2982 


9545 


3148 


9492 


3313 


9435 


39 


22 


2650 


9642 


2818 


9595 


29S5 


9544 


3151 


9491 


3316 


9434 


38 


23 


2653 


9642 


2821 


9594 


2988 


9543 


3154 


9490 


3319 


9433 


37 


24 


2656 


9641 


2823 


9593 


2990 


9542 


3156 


9489 


3322 


9432 


36 


25 


265S 


9640 


2826 


9592 


2993 


9542 


3159 


9488 


3324 


9431 


35 


26 


2661 


9639 


2829 


9591 


2996 


9541 


3162 


9487 


3327 


9430 


34 


27 


2664 


9639 


2832 


9591 


2999 


9540 


3165 


9486 


3330 


9429 


33 


2S 


2667 


9638 


2835 


9590 


3002 


9539 


3168 


9485 


3333 


9428 


32 


29 


2670 


9637 


2837 


9589 


3004 


9538 


3170 


9484 


3335 


9427 


31 


30 


2672 


9636 


2840 


9588 


3007 


9537 


3173 


9483 


3338 


9.426 


30 


31 


2675 


9636 


2843 


9587 


3010 


9536 


3176 


9482 


3341 


9425 


29 


32 


2678 


9635 


2846 


9587 


3013 


9535 


3179 


9481 


3344 


9424 


28 


33 


26S1 


9634 


2849 


9586 


3015 


9535 


3181 


9480 


3346 


9423 


27 


34 


2684 


9633 


2851 


9585 


3018 


9534 


3184 


9480 


3349 


9423 


26 


35 


2686 


9632 


2854 


9584 


3021 


9533 


3187 


9479 


3352 


9422 


25 


36 


2689 


9632 


2S57 


9583 


3024 


9532 


3190 


9478 


3355 


9421 


24 


37 


2692 


9631 


2S60 


95S2 


3026 


9531 


3192 


9477 


3357 


9420 


23 


38 


2695 


9630 


2862 


9582 


3029 


9530 


3195 


9476 


3360 


9419 


22 


39 


269S 


9629 


2865 


9581 


3032 


9529 


3198 


9475 


3363 


9418 


21 


40 


2700 


9628 


2868 


9580 


3035 


9528 


3201 


9474 


3365 


9417 


20 


41 


2703 


962S 


2871 


9579 


3038 


9527 


3203 


9473 


336S 


9416 


19 


42 


2706 


9627 


2874 


9578 


3040 


9527 


3206 


9472 


3371 


9415 


IS 


43 


2709 


9626 


2876 


9577 


3043 


9526 


3209 


9471 


3374 


9414 


17 


44 


2712 


9625 


2879 


9577 


3046 


9525 


3212 


9470 


3376 


9413 


16 


45 


2714 


9625 


2882 


9576 


3049 


9524 


3214 


9469 


3379 


9412 


15 


46 


2717 


9624 


2885 


9575 


3051 


9523 


3217 


9468 


3382 


9411 


14 


47 


2720 


9623 


2888 


9574 


3054 


9522 


3220 


9467 


3385 


9410 


13 


4S 


2723 


9622 


2890 


9573 


3057 


9521 


3223 


9466 


3387 


9409 


12 


49 


2726 


9621 


2893 


9572 


3060 


9520 


3225 


9466 


3390 


9408 


11 


50 


2728 


9621 


2896 


9572 


3062 


9520 


3228 


9465 


3393 


9407 


io 


51 


2731 


9620 


2899 


9571 


3065 


9519 


3231 


9464 


3396 


9406 


9 


52 


2734 


9619 


2901 


9570 


306S 


9518 


3234 


9463 


339S 


9405 


8 


53 


2737 


9618 


2904 


9569 


3071 


9517 


3236 


9462 


3401 


9404 


7 


54 


2740 


9617 


2907 


9568 


3074 


9516 


3239 


9461 


3404 


9403 


6 


55 


2742 


9617 


2910 


9567 


3076 


9515 


3242 


9460 


3407 


9402 


5 


56 


2745 


9616 


2913 


9566 


3079 


9514 


3245 


9459 


3409 


9401 


4 


57 


2748 


9615 


2915 


9566 


30S2 


9513 


3247 


9458 


3412 


9400 


3 


58 


2751 


9614 


2918 


9565 


3085 


9512 


3250 


9457 


3415 


9399 


2 


59 


2754 


9613 


2921 


9564 


3087 


9511 


3253 


9456 


3417 


9398 


1 


60 


2756 


9613 


2924 


9563 


3090 


9511 


3256 


9455 


3420 


9397 







cos 


sin 


cos 


sin 


cos 


sin 


cos 


sin 


cos 


sin 




t 


74° 


73° 


72° 


71° 


70° 


t 



56 



NATURAL SINES AND COSINES. 



/ 


20° 


21° 


22° 


23° 


24° 


r 




sin 


cos 


sin 


cos 


sin cos 


sin cos 


sin 


cos 




o 


3420 


9397 


3584 


9336 


3746 9272 


3907 9205 


4067 


9135 


60 


1 


3423 


9396 


3586 


9335 


3749 9271 


3910 9204 


4070 


9134 


59 


2 


3426 


9395 


3589 


9334 


3751 9270 


3913 9203 


4073 


9133 


58 


3 


3428 


9394 


3592 


9333 


3754 9269 


3915 9202 


4075 


9132 


57 


- 4 


3431 


9393 


3595 


9332 


3757 9267 


3918 9200 


4078 


9131 


56 


5 


3434 


9392 


3597 


9331 


3760 9266 


3921 9199 


4081 


9130 


55 


6 


3437 


9391 


3600 


9330 


3762 9265 


3923 9198 


4083 


9128 


54 


7 


3439 


9390 


3603 


9328 


3765 9264 


3926 9197 


4086 


9127 


53 


8 


3442 


9389 


3605 


9327 


3768 9263 


3929 9196 


4089 


9126 


52 


9 


3445 


9388 


3608 


9326 


3770 9262 


3931 9195 


4091 


9125 


51 


10 


3448 


9387 


3611 


9325 


3773 9261 


3934 9194 


4094 


9124 


50 


11 


3450 


9386 


3614 


9324 


3776 9260 


3937 9192 


4097 


9122 


49 


12 


3453 


9385 


3616 


9323 


3778 9259 


3939 9191 


4099 


9121 


48 


13 


3456 


9384 


3619 


9322 


3781 9258 


3942 9190 


4102 


9120 


47 


14 


3458 


9383 


3622 


9321 


3784 9257 


3945 9189 


4105 


9119 


46 


15 


3461 


9382 


3624 


9320 


3786 9255 


3947 9188 


4107 


9118 


45 


16 


3464 


9381 


3627 


9319 


3789 9254 


3950 '9187 


4110 


9116 


44 


17 


' 3467 


9380 


3630 


9318 


3792 9253 


3953 9186 


4112 


9115 


43 


18 


3469 


9379 


3633 


9317 


3795 9252 


3955 9184 


4115 


9114 


42 


19 


3472 


9378 


3635 


9316 


3797 9251 


3958 9183 


4118 


9113 


41 


20 


3475 


9377 


3638 


9315 


3800 9250 


3961 9182 


4120 


9112 


40 


21 


3478 


9376 


3641 


9314 


3803 9249 


3963 9181 


4123 


9110 


39 


22 


3480 


9375 


3643 


9313 


3805 9248 


3966 9180 


4126 


9109 


38 


23 


3483 


9374 


3646 


9312 


3808 9247 


3969 9179 


4128 


9108 


37 


24 


3486 


9373 


3649 


9311 


3811 9245 


3971 9178 


4131 


9107 


36 


25 


3488 


9372 


3651 


9309 


3813 9244 


3974 9176 


4134 


9106 


35 


26 


3491 


9371 


3654 


9308 


3816 9243 


3977 9175 


4136 


9104 


34 


27 


3494 


9370 


3657 


9307 


3819 9242 


3979 9174 


4139 


9103 


33 


28 


3497 


9369 


3660 


9306 


3821 9241 


3982 9173 


4142 


9102 


32 


29 


3499 


9368 


3662 


9305 


3824 9240 


5985 9172 


4144 


9101 


31 


30 


3502 


9367 


3665 


9304 


3827 9239 


' 3987 9171 


4147 


9100 


30 


31 


3505 


9366 


3668 


9303 


3830 9238 


3990 9169 


4150 


9098 


29 


32 


3508 


9365 


3670 


9302 


3832 9237 


3993 9168 


4152 


9097 


28 


33 


3510 


9364 


3673 


9301 


3835 9235 


3995 9167 


4155 


9096 


27 


34 


3513 


9363 


3676 


9300 


3838 9234 


3998 9166 


4158 


9095 


26 


35 


3516 


9362 


3679 


9299 


3840 9233 


4001 9165. 


4160 


9094 


25 


36 


3518 


9361 


3681 


9298 


3843 9232 


4003 9164 


4163 


9092 


24 


37 


3521 


9360 


3684 


9297 


3846 9231 


4006 9162 


4165 


9091 


23 


38 


3524 


9359 


3687 


9296 


3848 9230 


4009 9161 


4168 


9090 ■ 


22 


39 


3527 


9358 


3689 


9295 


3851 9229 


4011 9160 


4171 


9088 


21 


40 


3529 


9356 


3692 


9293 


3854-9228 


4014 9159 


4173 


9088 


20 


41 


3532 


9355 


3695 


9292 


3856 9227 


4017 9158 


4176 


9086 


19 


42 


3535 


9354 


3697 


9291 


3859 9225 


4019 9157 


4179 


9085 


18 


43 


3537 


9353 


3700 


9290 


3862 9224 


4022 9155 


4181 


9084 


17 


44 


3540 


9352 


3703 


9289 


3864 9223 


4025 9154 


4184 


9083 


16 


45 


3543 


9351 


3706 


9288 


3867 9222 


4027 9153 


4187 


9081 


15 


46 


3546 


9350 


3708 


9287 


3870 9221 


4030 9152 


4189 


9080 


14 


47 


3548 


9349 


3711 


9286. 


3872 9220 


4033 9151 


4192 


9079 


13 


48 


3551 


9348 


3714 


9285 


3875 9219 


4035 9150 


4195 


9078 


12 


49 


3554 


9347 


3716 


9284 


- 3878 9218 


4038 9148 


4197 


9077 


11 


50 


3557 


9346 


3719 


9283 


3881 9216 


4041 9147 


4200 


9075 


10 


51 


3559 


9345 


3722 


9282 ■ 


3883 9215 


4043 9146 


4202 


9074 


9 


52 


3562 


9344 


3724 


9281 


3886 9214 


4046 9145 


4205 


9073 


8 


53 


3565 


9343 


3727 


9279 


3889 9213 


4049 9144 


4208 


9072 


7 


54 


3567 


9342 


3730 


9278 


"3891 9212 


4051 9143 


4210 


9070 


6 


55 


3570 


9341 


3733 


9277 


3894 9211 


4054 9141 


4213 


9069 


5 


56 


3573 


9340 


3735 


9276 


3S97 9210 


4057 9140 


4216 


9068 


4 


57 


3576 


9339 


3738 


9275 


3S99 9208 


4059 9139 


4218 


9067 


3 


58 


3578 


9338 


3741 


9274 


3902 9207 


4062 9138 


4221 


9066 


2 


59 


3581 


9337 


3743 


9273 


3905 9206 


4065 9137 


4224 


9064 


1 


60 


3584 


9336 


3746 


9272 


3907 9205 


4067 9135 


4226 


9063 







cos 


sin 


cos 


sin 


cos sin 


cos sin 


cos 


sin 




t 


69° 


68° 


67° 


66° 


65° 


; 



NATURAL SINES AND COSINES. 



57 



t 


25° 


26° 

sin cos 


2 


1° 


28° 


29° 


t 




sin 


cos 


sin 


cos 


sin 


cos 


sin 


cos 







4226 


9063 


4384 


S98S 


4540 


8910 


4695 


8S29 


4848 


8746 


60 


1 


4229 


9062 


4386 


S987 


4542 


8909 


4697 


8828 


4851 


8745 


59 


2 


4231 


9061 


4389 


S9S5 


4545 


8907 


4700 


8827 


4853 


8743 


58 


3 


4234 


9059 


4392 


89S4 


4548 


8906 


4702 


8825 


4856 


8742 


57 


4 


4237 


9058 


4394 


8983 


4550 


8905 


4705 


8824 


4858 


8741 


56 


5 


4239 


9057 


4397 


S9S2 


4553 


8903 


470S 


8823 


4861 


8739 


55 


6 


4242 


9056 


4399 


8980 


4555 


8902 


4710 


8821 


4863 


873S 


54 


7 


4245 


9054 


4402 


8979 


4558 


8901 


4713 


8820 


4866 


8736 


53 


8 


4247 


9053 


4405 


897S 


4561 


8899 


4715 


8819 


486S 


8735 


52 


9 


-4250 


9052 


4407 


8976 


4563 


8S98 


4718 


8817 


4871 


8733 


51 


10 


4253 


9051 


4410 


8975 


4566 


8897 


4720 


8816 


4874 


8732 


50 


11 


4255 


9050 


4412 


8974 


4568 


8895 


4723 


8814 


4876 


8731 


49 


12 


425S 


9048 


4415 


8973 


4571 


8894 


4726 


8813 


4879 


8729 


48 


13 


4260 


9047 


4418 


8971 


4574 


SS93 


4728 


8812 


4881 


8728 


47 


14 


4263 


9046 


4420 


8970 


4576 


8892 


4731 


8810 


4884 


8726 


46 


15 


4266 


9045 


4423 


8969 


4579 


8890 


4733 


8809 


4886 


8725 


45 


16 


4268 


9043 


4425 


S967 


45S1 


8889 


4736 


8808 


4889 


8724 


44 


17 


4271 


9042 


4428 


8966 


4584 


888S 


4738 


8806 


4891 


8722 


43 


18 


4274 


9041 


4431 


8965 


4586 


8SS6 


4741 


8805 


4894 


8721 


42 


19 


4276 


9040 


4433 


8964 


4589 


8885 


4743 


8803 


4896 


8719 


41 


20 


4279 


9038 


4436 


8962 


4592 


8884 


4746 


8802 


4899 


8718 


40 


21 


42S1 


9037 


4439 


8961 


4594 


S882 


4749 


8801 


4901 


8716 


39 


22 


4284 


9036 


4441 


8960 


4597 


8881 


4751 


8799 


4904 


8715 


38 


23 


4287 


9035 


4444 


8958 


4599 


8879 


4754 


8798 


4907 


8714 


37 


24 


4289 


9033 


4446 


8957 


4602 


8878 


4756 


8796 


4909 


8712 


36 


25 


4292 


9032 


4449 


8956 


4605 


8877 


4759 


8795 


4912 


8711 


35 


26 


4295 


9031 


4452 


8955 


4607 


8875 


4761 


8794 


4914 


8709 


34 


27 


4297 


9030 


4454 


8953 


4610 


8874 


4764 


8792 


4917 


8708 


33 


• 28 - 


4300 


9028 


4457 


8952 


4612 


8873 


4766 


8791 


4919 


8706 


32 


29 


4302 


9027 


4459 


8951 


4615 


8871 


4769 


8790 


4922 


8705 


31 


30 


4305 


9026 


4462 


8949 


4617 


8870 


4772 


8788 


4924 


8704 


30 


31 


430S 


9025 


4465 


8948 


4620 


8869 


4774 


8787 


4927 


8702 


29 


32 


4310 


9023 


4467 


8947 


4623 


8867 


4777 


8785 


4929 


8701 


28 


33 


4313 


9022 


4470 


8945 


4625 


8866 


4779 


8784 


4932 


8699 


27 


34 


4316 


9021 


4472 


8944 


4628 


8865 


4782 


8783 


4934 


8698 


26 


35 


4318 


9020 


4475 


8943 


4630 


8863 


4784 


8781 


4937 


8696 


25 


36 


'4321 


9018 


4478 


8942 


4633 


8862 


4787 


8780 


4939 


8695 


24 


37 


4323 


9017 


4480 


8940 


4636 


8861 


4789 


8778 


4942 


8694 


23 


38 


4326 


9016 


4483 


8939 


4638 


8859 


4792 


8777 


4944 


8692 


22 


39 


4329 


9015 


4485 


8938 


4641 


8858 


4795 


8776 


4947 


8691 


21 


40 


4331 


9013 


4488 


8936 


4643 


SS57 


4797 


8774 


4950 


8689 


20 


41 


4334 


9012 


4491 


8935 


4646 


8855 


4800 


8773 


4952 


8688 


19 


42 


4337 


9011 


4493 


8934 


4648 


8854 


4802 


8771 


4955 


8686 


IS 


43 


4339 


9010 


4496 


8932 


4651 


8853 


4805 


8770 


4957 


8685 


17 


44 


4342 


9008 


4498 


8931 


4654 


8851 


4807 


8769 


4960 


8683 


16 


45 


4344 


9007 


4501 


8930 


4656 


8850 


4810 


8767 


4962 


8682 


15 


46 


4347 


9006 


4504 


8928 


4659 


8849 


4812 


8766 


4965 


8681 


14 


47 


4350 


9004 


4506 


8927 


4661 


8847 


4815 


S764 


4967 


8679 


13 


48 


4352 


9003 


4509 


8926 


4664 


8846 


4818 


8763 


4970 


8678 


12 


49 


4355 


9002 


4511 


8925 


4666 


8844 


4820 


8762 


4972 


8676 


11 


50 


4358 


9001 


4514 


8923 


4669 


8843 


4823 


S760 


4975 


8675 


10 


51 


4360 


8999 


4517 


8922 


4672 


8S42 


4825 


8759 


4977 


8673 


9 


52 


4363 


8998 


4519 


8921 


4674 


8840 


482S 


8757 


4980 


8672 


8 


53 


4365 


8997 


4522 


8919 


4677 


8839 


4830 


8756 


4982 


8670 


7 


54 


4368 


8996 


4524 


8918 


4679 


8838 


4833 


8755 


4985 


8669 


6 


55 


4371 


8994 


4527 


8917 


4682 


8836 


4835 


8753 


4987 


8668 


5 


56 


4373 


8993 


4530 


8915 


4684 


SS35 


4838 


8752 


4990 


8666 


4 


57 


4376 


8992 


4532 


8914 


46S7 


8834 


4840 


8750 


4992 


8665 


3 


5S 


4378 


8990 


4535 


8913 


4690 


8832 


4843 


8749 


4995 


8663 


2 


59 


4381 


8989 


4537 


8911 


4692 


S831 


4846 


8748 


4997 


8662 


1 


60 


4384 


S9S8 


4540 


8910 


4695 


8829 


4848 


8746 


5000 


8660 


O 




cos 


sin 


cos 


sin 


cos 


sin 


cos 


sin 


cos 


sin 




r 


64° 


63° 


6: 


2° 


61° 


60° 


t 



58 



NATURAL SINES AND COSINES. 



/ 


30° 


31° 


32° 


33° 

sin cos 


34° 


t 




sin 


cos 


sin 


cos 


sin cos 


sin 


cos 







5000 


8660 


5150 


8572 


5299 8480 


5446 


8387 


5592 


8290 


60 


1 


5003 


8659 


5153 


8570 


5302 8479 


5449 


8385 


5594 


8289 


59 


2 


5005 


8657 


5155 


8569 


5304 8477 


5451 


8384 


5597 


8287 


58 


3 


5008 


8656 


5158 


8567 


5307 8476 


5454 


8382 


5599 


8285 


57 


■ 4 


5010 


8654 


5160 


8566 


5309 S474 


5456 


83S0 


5602 


8284 


56 


5 


5013 


8653 


5163 


8564 


5312 8473 


5459 


8379 


5604 


82S2 


55 


6 


5015 


8652 


5165 


S563 


5314 8471 


5461 


8377 


5606 


8281 


54 


7 


5018 


8650 


5168 


S561 


5316 8470 


5463 


8376 


5609 


8279 


53 


8 


5020 


8649 


5170 


8560 


5319 8468 


5466 


8374 


5611 


8277 


52 


9 


5023 


8647 


5173 


8558 


5321 8467 


5468 


8372 


5614 


8276 


51 


10 


5025 


8646 


5175 


8557 


5324 8465 


5471 


8371 


5616 


8274 


50 


11 


5028 


8644 


5178 


8555 


5326 8463 


5473 


8369 


5618 


8272 


49 


12 


5030 


8643 


5180 


8554 


5329 8462 


5476 


8368 


5621 


8271 


48 


13 


5033 


8641 


5183 


8552 


5331 8460 


5478 


8366 


5623 


8269 


47 


14 


5035 


8640 


5185 


8551 


5334 8459 


5480 


8364 


5626 


8268 


46 


15 


5038 


8638 


5188 


8549 


5336 8457 


5483 


8363 


5628 


8266 


45 


16 


5040 


8637 


5190 


8548 


5339 8456 


5485 


'8361 


5630 


8264 


44 


17 


5043 


8635 


5193 


8546 


5341 8454 


5488 


8360 


5633 


8263 


43 


18 


5045 


8634 


5195 


8545 


5344 8453 


5490 


8358 


5635 


8261 


42 


19 


5048 


8632 


5198 


8543 


5346 8451 


5493 


8356 


5638 


8259 


41 


20 


5050 


8631 


5200 


8542 


5348 8450 


5495 


8355 


5640 


8258 


40 


21 


5053 


8630 


5203 


8540 


5351 8448 


5498 


8353 


5642 


8256 


39 


22 


5055 


8628 


5205 


8539 


5353 8446 


5500 


8352 


5645 


8254 


38 


23 


5058 


8627 


5208 


8537 


5356 8445 


5502 


8350 


5647 


8253 


37 


24 


5060 


8625 


5210 


8536 


5358 8443 


5505 


8348 


5650 


8251 


36 


25 


5063 


8624 


5213 


8534 


5361 8442 


5507 


8347 


5652 


8249 


35 


26 


5065 


8622 


5215 


8532 


5363 8440 


5510 


8345 


5654 


8248 


34 


27 


5068 


8621 


5218 


8531 


5366 8439 


5512 


8344 


5657 


8246 


33 


28 


5070 


8619 


5220 


8529 


5368 8437 


5515 


8342 


5659 


8245 


32. 


29 


5073 


861 S 


5223 


8528 


5371 8435 


4517 


8340 


5662 


8243 


31 


30 


5075 


8616 


5225 


8526 


5373 8434 


'5519 


8339 


5664 


8241 


30 


31 


5078 


8615 


5227 


8525 


5375 8432 


5522 


8337 


5666 


8240 


29 


32 


5080 


8613 


5230 


8523 


5378 8431 


5524 


8336 


5669 


8238 


28 


33 


5083 


8612 


5232 


8522 


5380 8429 


5527 


8334 


5671 


8236 


27 


34 


5085 


8610 


5235 


8520 


5383 8428 


5529 


8332 


5674 


8235 


26 


35 


5088 


8609 


5237 


8519 


5385 8426 


5531 


8331 


5676 


8233 


25 


36 


5090 


8607 


5240 


8517 


5388 8425 


5534 


8329 


5678 


8231 


24 


37 


5093 


8606 


5242 


8516 


5390 8423 


5536 


8328 


5681 


8230 


23 


38 


5095 


8604 


5245 


8514 


5393 8421 


5539 


8326 


5683 


8228 ■ 


22 


39 


509S 


8603 


5247 


8513 


5395 8420 


5541 


8324 


5686 


8226 


21 


40 


5100 


8601 


5250 


8511 


5398 -8418 


5544 


8323 


5688 


8225 


20 


41 


5103 


8600 


5252 


8510 


5400 8417 


5546 


8321 


5690 


8223 


19 


42 


5105 


8599 


5255 


8508 


5402 8415 


5548 


8320 


5693 


8221 


IS 


43 


5108 


8597 


5257 


8507 


5405 8414 


5551 


8318 


5695 


8220 


17 


44 


5110 


8596 


5260 


8505 


5407 8412 


5553 


8316 


5698 


8218 


16 


45 


5113 


8594 


5262 


8504 


5410 8410 


5556 


S315 


5700 


8216 


15 


46 


5115 


8593 


5265 


8502 


5412 S409 


5558 


8313 


5702 


S215 


14 


47 


5118 


8591 


5267 


8500 


5415. 8407 


5561 


8311 


5705 


8213 


13 


48 


5120 


8590 


5270 


8499 


5417 8406 


5563 


8310 


5707 


8211 


12 


49 


5123 


8588 


5272 


8497 


- 5420 8404 


5565 


8308 


5710 


8210 


11 


50 


5125 


8587 


5275 


8496 


5422 8403 


5568 


8307 


5712 


8208 


10 


51 


5128 


8585 


5277 


8494 


5424 8401 


5570 


8305 


5714 


8207 


9 


52 


5130 


8584 


5279 


8493 


5427 8399 


5573 


S303 


5717 


8205 


8 


53 


5133 


8582 


5282 


8491 


5429 839S 


5575 


8302 


5719 


8203 


7 


54 


5135 


8581 


5284 


8490 


-5432 S396 


5577 


8300 


5721 


8202 


6 


55 


5138 


8579 


5287 


8488 


5434 8395 


5580 


8299 


5724 


8200 


5 


56 


5140 


8578 


52S9 


8487 


5437 8393 


5582 


S297 


5726 


8198 


4 


57 


5143 


8576 


5292 


8485 


5439 8391 


5585 


8295 


5729 


8197 


3 


58 


5145 


8575 


5294 


8484 


5442 8390 


5587 


8294 


5731 


8195 


2 


59 


514S 


8573 


5297 


S482 


5444 8388 


5590 


8292 


5733 


8193 


1 


60 


5150 


8572 


5299 


8480 


5446 8387 


5592 


8290 


5736 


8192 







cos 


sin 


cos 


sin 


cos sin 


cos 


sin 


cos 


sin 




r 


59° 


58° 


57° 


56° 


55° 


t 



NATURAL SINES AND COSINES. 



59 



/ 


35° 


36° 


37° 


38° 


39° 


t 




sin 


cos 


sin 


cos 


sin 


cos 


sin 


cos 


sin 


cos 







5736 


8192 


5878 


8090 


6018 


7986 


6157 


7880 


6293 


7771 


60 


1 


5738 


8190 


5880 


8088 


6020 


7985 


6159 


7878 


6295 


7770 


59 


2 


5741 


8188 


5883 


8087 


6023 


7983 


6161 


7877 


6298 


7768 


58 


3 


5743 


8187 


5885 


8085 


6025 


7981 


6163 


7875 


6300 


7766 


57 


4 


5745 


8185 


5887 


8083 


6027 


7979 


6166 


7873 


6302 


7764 


56 


5 


5748 


8183 


5890 


8082 


6030 


7978 


6168 


7871 


6305 


7762 


55 


6 


5750 


8181 


5892 


8080 


6032 


7976 


6170 


7869 


6307 


7760 


54 


7 


5752 


S180 


5894 


S07S 


6034 


7974 


6173 


7868 


6309 


7759 


53 


8 


5755 


8178 


5897 


8076 


6037 


7972 


6175 


7866 


6311 


7757 


52 


9 


- 5757 


8176 


5899 


S075 


6039 


7971 


6177 


7864 


6314 


7755 


51 


10 


5760 


8175 


5901 


8073 


6041 


7969 


6180 


7862 


6316 


7753 


50 


11 


5762 


8173 


5904 


8071 


6044 


7967 


6182 


7860 


6318 


7751 


49 


12 


5764 


S171 


5906 


8070 


6046 


7965 


6184 


7859 


6320 


7749 


48 


13 


5767 


8170 


590S 


8068 


6048 


7964 


6186 


7857 


6323 


7748 


47 


14 


5769 


8168 


5911 


8066 


6051 


7962 


6189 


7855 


6325 


7746 


46 


15 


5771 


8166 


5913 


8064 


6053 


7960 


6191 


7853 


6327 


7744 


45 


16 


5774 


8165 


5915 


8063 


6055 


7958 


6193 


7851 


6329 


7742 


44 


17 


5776 


8163 


5918 


8061 


6058 


7956 


6196 


7850 


6332 


7740 


43 


18 


5779 


8161 


5920 


8059 


6060 


7955 


6198 


7848 


6334 


7738 


42 


19 


5781 


8160 


5922 


8058 


6062 


7953 


6200 


7346 


6336 


7737 


41 


20 


5783 


8158 


5925 


8056 


6065 


7951 


6202 


7844 


6338 


7735 


40 


21 


5786 


8156 


5927 


8054 


6067 


7950 


6205 


7842 


6341 


7733 


39 


22 


5788 


8155 


5930 


8052 


6069 


7948 


6207 


7841 


6343 


7731 


38 


23 


5790 


8153 


5932 


8051 


6071 


7946 


6209 


7839 


6345 


7729 


37 


24 


5793 


8151 


5934 


8049 


6074 


7944 


6211 


7837 


6347 


7727 


36 


25 


5795 


8150 


5937 


8047 


6076 


7942 


6214 


7835 


6350 


7725 


35 


26 


5798 


8148 


5939 


8045 


6078 


7941 


6216 


7833 


6352 


7724 


34 


27 


5800 


8146 


5941 


8044 


60S1 


7939 


6218 


7832 


6354 


7722 


33 


28 - 


5802 


8145 


5944 


8042 


6083 


7937 


6221 


7830 


6356 


7720 


32 


29 


5805 


8143 


5946 


8040 


6085 


7935 


6223 


7828 


6359 


7718 


31 


30 


5807 


8141 


5948 


8039 


6088 


7934 


6225 


7826 


6361 


7716 


30 


31 


5809 


8139 


5951 


8037 


6090 


7932 


6227 


7824 


6363 


7714 


29 


32 


5812 


8138 


5953 


8035 


6092 


7930 


6230 


7822 


6365 


7713 


28 


33 


5814 


8136 


5955 


8033 


6095 


7928 


6232 


7821 


6368 


7711 


27 


34 


5816 


8134 


5958 


8032 


6097 


7926 


6234 


7819 


6370 


7709 


26 


35 


5819 


8133 


5960 


8030 


6099 


7925 


6237 


7817 


6372 


7707 


25 


36 


'5821 


8131 


5962 


8028 


6101 


7923 


6239 


7815 


6374 


7705 


24 


37 


5824 


8129 


5965 


8026 


6104 


7921 


6241 


7813 


9376 


7703 


23 


38 


5826 


8128 


5967 


8025 


6106 


7919 


6243 


7812 


6379 


7701 


22 


39 


5828 


8126 


5969 


8023 


6108 


7918 


6246 


7810 


6381 


7700 


21 


40 


5831 


8124 


5972 


8021 


6111 


7916 


6248 


7808 


6383 


7698 


20 


41 


5833 


8123 


5974 


8020 


6113 


7914 


6250 


7806 


6385 


7696 


19 


42 


5835 


8121 


5976 


8018 


6115 


7912 


6252 


7804 


6388 


7694 


IS 


43 


5838 


8119 


5979 


8016 


6118 


7910 


6255 


7802 


6390 


7692 


17 


44 


5840 


8117 


5981 


8014 


6120 


7909 


6257 


7801 


6392 


7690 


16 


45 


5842 


8116 


5983 


8013 


6122 


7907 


6259 


7799 


6394 


7688 


15 


46 


5845 


8114 


5986 


8011 


6124 


7905 


6262 


7797 


6397 


7687 


14 


47 


5847 


8112 


5988 


8009 


6127 


7903 


6264 


7795 


6399 


7685 


13 


48 


5850 


8111 


5990 


8007 


6129 


7902 


6266 


7793 


6401 


7683 


12 


49 


5852 


8109 


5993 


8006 


6131 


7900 


6268 


7792 


6403 


7681 


11 


50 


5854 


8107 


5995 


8004 


6134 


7898 


6271 


7790 


6406 


7679 


10 


51 


5857 


8106 


5997 


8002 


6136 


7896 


6273 


7788 


6408 


7677 


9 


52 


5859 


8104 


6000 


8000 


6138 


7894 


6275 


7786 


6410 


7675 


8 


53 


5861 


8102 


6002 


7999 


6141 


7893 


6277 


7784 


6412 


7674 


7 


54 


5864 


8100 


6004 


7997 


6143 


7891 


6280 


7782 


6414 


7672 


6 


55 


5866 


8099 


6007 


7995 


6145 


7889 


6282 


7781 


6417 


7670 


5 


56 


5S68 


8097 


6009 


7993 


6147 


7887 


6284 


7779 


6419 


7668 


4 


57 


5871 


8095 


6011 


7992 


6150 


7885 


6286 


7777 


6421 


7666 


3 


58 


5873 


8094 


6014 


7990 


6152 


7884 


6289 


7775 


6423 


7664 


2 


59 


5875 


8092 


6016 


7988 


6154 


7882 


6291 


7773 


6426 


7662 


1 


60 


5878 


8090 


6018 


7986 


6157 


7880 


6293 


7771 


6428 


7660 







cos 


sin 


cos 


sin 


cos 


sin 


cos 


sin 


cos 


sin 




t 


54° 


53° 


52° 


51° 


50° 


r 



60 



NATURAL SINES AND COSINES. 



/ 


40° 


41° 


42° 


43° 


44° 


t 




sin 


cos 


sin 


cos 


sin 


cos 


sin 


cos 


sin 


cos. 







6428 


7660 


6561 


7547 


6691 


7431 


6820 


7314 


6947 


7193 


60 


1 


6430 


7659 


6563 


7545 


6693 


7430 


6822 


7312 


6949 


7191 


59 


2 


6432 


7657 


6565 


7543 


6696 


7428 


6824 


7310 


6951 


7189 


58 


3 


6435 


7655 


6567 


7541 


6698 


7426 


6826 


7308 


6953 


7187 


57 


• 4 


6437 


7653 


6569 


7539 


6700 


7424 


6828 


7306 


6955 


7185 


56 


5 


6439 


7651 


6572 


7538 


6702 


7422 


6831 


7304 


6957 


7183 


55 


6 


6441 


7649 


6574 


7536 


6704 


7420 


6833 


7302 


6959 


7181 


54 


7 


6443 


7647 


6576 


7534 


6706 


7418 


6835 


7300 


6961 


7179 


53 


8 


6446 


7645 


6578 


7532 


6709 


7416 


6837 


7298 


6963 


7177 


52 


9 


6448 


7644 


6580 


7530 


6711 


7414 


6839 


7296 


6965 


7175 


51 


10 


6450 


7642 


6583 


7528 


6713 


7412 


6841 


7294 


6967 


7173 


50 


11 


6452 


7640 


6585 


7526 


6715 


7410 


6843 


7292 


6970 


7171 


49 


12 


6455 


7638 


6587 


7524 


6717 


7408 


6845 


7290 


6972 


7169 


48 


13 


6457 


7636 


6589 


7522 


6719 


7406 


6848 


7288 


6974 


7167 


47 


14 


6459 


7634 


6591 


7520 


6722 


7404 


6850 


7286 


6976 


7165 


46 


15 


6461 


7632 


6593 


7518 


6724 


7402 


6852 


7284 


6978 


7163 


45 


16 


6463 


7630 


6596 


7516 


6726 


7400 


6854 


■7282 


6980 


7161 


44 


17 


6466 


7629 


6598 


7515 


6728 


7398 


6856 


7280 


6982 


7159 


43 


18 


6468 


7627 


6600 


7513 


6730 


7396 


6858 


7278 


6984 


7157 


42 


19 


6470 


7625 


6602 


7511 


6732 


7394 


6860 


7276 


6986 


7155 


41 


20 


6472 


7623 


6604 


7509 


6734 


7392 


6862 


7274 


6988 


7153 


40 


21 


6475 


7621 


6607 


7507 


6737 


7390 


6865 


7272 


6990 


7151 


39 


22 


6477 


7619 


6609 


7505 


6739 


7388 


6867 


7270 


6992 


7149 


38 


23 


6479 


7617 


6611 


7503 


6741 


7387 


6869 


7268 


6995 


7147 


37 


24 


6481 


7615 


6613 


7501 


6743 


7385 


6871 


7266 


6997 


7145 


36 


25 


6483 


7613 


6615 


7499 


6745 


7383 


6873 


7264 


6999 


7143 


35 


26 


6486 


7612 


6617 


7497 


6747 


7381 


6875 


7262 


7001 


7141 


34 


27 


6488 


7610 


6620 


7495 


6749 


7379 


6877 


7260 


7003 


7139 


33 


28 


6490 


760S 


6622 


7493 


6752 


7377 


6879 


7258 


7005 


7137 


31 


29 


6492 


7606 


6624 


7491 


6754 


7375 


£831 


7256 


7007 


7135 


31 


30 


6494 


7604 


6626 


7490 


6756 


7373 


•68S4 


7254 


7009 


7133 


30 


31 


6497 


7602 


6628 


7488 


6758 


7371 


6886 


72'52 


7011 


7130 


29 


32 


6499 


7600 


6631 


7486 


6760 


7369 


6888 


7250 


7013 


7128 


28 


33 


6501 


7598 


6633 


7484 


6762 


7367 


6890 


7248 


7015 


7126 


27 


34 


6503 


7596 


6635 


7482 


6764 


7365 


6892 


7246 


7017 


7124 


26 


35 


6506 


7595 


6637 


7480 


6767 


7363 


6894 


7244 


7019 


7122 


25 


36 


6508 


7593 


6639 


7478 


6769 


7361 


6896 


7242 


7022 


7120 


24 


37 


6510 


7591 


6641 


7476 


6771 


7359 


6898 


7240 


7024 


7118 


23 


38 


6512 


7589 


6644 


7474 


6773 


7357 


6900 


7238 


7026 


7116 


22 


39 


6514 


7587 


6646 


7472 


6775 


7355 


6903 


7236 


7028 


7114 


21 


40 


6517 


7585 


6648 


7470 


6777 


7253 


6905 


7234 


7030 


7112 


20 


41 


6519 


7583 


6650 


7468 


6779 


7351 


6907 


7232 


7032 


7110 


19 


42 


6521 


7581 


6652 


7466 


6782 


7349 


6909 


7230 


7034 


7108 


IS 


43 


6523 


7579 


6654 


7464 


6784 


7347 


6911 


7228 


7036 


7106 


17 


44 


6525 


7578 


6657 


7463 


6786 


7345 


6913 


7226 


7038 


7104 


16 


45 


6528 


7576 


6659 


7461 


6788 


7343 


6915 


7224 


7040 


7102 


15 


46 


6530 


7574 


6661 


7459 


6790 


7341 


6917 


7222 


7042 


7100 


14 


47 


6532 


7572 


6663 


7457 


6792 


7339 


6919 


7220 


7044 


7098 


13 


48 


6534 


7570 


6665 


7455 ■ 


6794 


7337 


6921 


7218 


7046 


7096 


12 


49 


6536 


7568 


6667 


7453 


6797 


7335 


6924 


7216 


7048 


7094 


11 


50 


6539 


7566 


6670 


7451 


6799 


7333 


6926 


7214 


7050 


7092 


10 


51 


6541 


7564 


6672 


7449 


6S01 


7331 


6928 


7212 


7053 


7090 


9 


52 


6543 


7562 


6674 


7447 


6803 


7329 


6930 


7210 


7055 


7088 


8 


53 


6545 


7560 


6676 


7445 


6805 


7327 


6932 


7208 


7057 


7085 


7 


54 


6547 


7559 


6678 


7443 


-6807 


7325 


6934 


7206 


7059 


7083 


6 


55 


6550 


7557 


6680 


7441 


6809 


7323 


6936 


7203 


7061 


7081 


5 


56 


6552 


7555 


6683 


7439 


6811 


7321 


693S 


7201 


7063 


7079 


4 


57 


6554 


7553 


6685 


7437 


6814 


7319 


6940 


7199 


7065 


7077 


3 


58 


6556 


7551 


6687 


7435 


6816 


7318 


6942 


7197 


7067 


7075 


2 


59 


6558 


7549 


6689 


7433 


6818 


7316 


6944 


7195 


7069 


7073 


1 


60 


6561 


7547 


6691 


7431 


6820 


7314 


6947 


7193 


7071 


7071 


O 




cos 


sin 


cos 


sin 


cos 


sin 


cos 


sin 


cos 


sin 




t 


49° 


48° 


47° 


46° 


45° 


r 



NATUKAL TANGENTS AND COTANGENTS. 61 



t 




0° 


1° 




2° 




3° 




4° 


r 


tan 


cot 


tan cot 


tan 


cot 


tan 


cot 


tan 


cot 





0000 


Infinite 


0175 57.2900 


0349 


28.6363 


0524 


19.0811 


0699 


14.3007 


60 


1 


0003 


3437.75 


0177 56.3506 


0352 


28.3994 


0527 


18.9755 


0702 


14.2411 


59 


2 


0006 


1718.87 


0180 55.4415 


0355 


28.1664 


0530 


IS 8711 


0705 


14.1821 


58 


3 


0009 


1145.92 


0183 54.5613 


0358 


27.9372 


0533 


18.7678 


0708 


14.1235 


57 


4 


0012 


859.436 


0186 53.7086 


0361 


27.7117 


0536 


186656 


0711 


140655 


56 


5 


0015 


687.549 


0189 52.8821 


0364 


27.4S99 


0539 


18.5645 


0714 


140079 


55 


6 


0017 


572.957 


0192 52.0807 


0367 


27.2715 


0542 


1S.4645 


0717 


13.9507 


54 


7 


0020 


491.106 


0195 51.3032 


0370 


27.0566 


0544 


18.3655 


0720 


13.8940 


53 


8 


0023 


429.718 


0198 50.5485 


0373 


26.8450 


0547 


18.2677 


0723 


13 8378 


52 


9 


0026 


3S1.971 


0201 49.8157 


0375 


26.6367 


0550 


18.1708 


0726 


13.7S21 


51 


10 


0029 


343.774 


0204 49.1039 


03 7S 


26.4316 


0553 


18.0750 


0729 


13.7267 


50 


11 


0032 


312521 


0207 48.4121 


0381 


26.2296 


0556 


179S02 


0731 


13.6719 


49 


12 


0035 


286.478 


0209 47.7395 


0384 


26.0307 


0559 


17.8863 


0734 


13.6174 


48 


13 


0038 


264.441 


0212 47.0S53 


0387 


25.S348 


0562 


17.7934 


0737 


13.5634 


47 


14 


0041 


245.552 


0215 46.4489 


0390 


25.6418 


0565 


17.7015 


0740 


13.5098 


46 


15 


0044 


229.1S2 


0218 45.8294 


0393 


25.4517 


056S 


17.6106 


0743 


13.4566 


45 


16 


0047 


214.858 


0221 45.2261 


0396 


25.2644 


0571 


17.5205 


0746 


13.4039 


44 


17 


0049 


202.219 


0224 44.6386 


0399 


25.0798 


0574 


17.4314 


0749 


13.3515 


43 


IS 


0052 


190.984 


0227 44.0661 


0402 


24.8978 


0577 


17.3432 


0752 


13.2996 


42 


19 


0055 


180.932 


0230 43.5081 


0405 


24.7185 


0580 


17.2558 


0755 


13.2480 


41 


20 


0058 


171.885 


0233 42.9641 


0407 


24.5418 


0582 


17.1693 


075S 


13.1969 


40 


21 


OOol 


163.700 


0236 42.4335 


0410 


24.3675 


0585 


17.0837 


0761 


13.1461 


39 


22 


0064 


156.259 


0239 41.9158 


0413 


24.1957 


05 88 


16.9990 


0764 


13.0958 


38 


23 


0067 


149.465 


0241 41.4106 


0416 


24.0263 


0591 


169150 


0767 


13.0458 


37 


24 


0070 


143.237 


0244 40.9174 


0419 


23.8593 


0594 


16.8319 


0769 


12.9962 


36 


25 


0073 


137507 


0247 40.435S 


0422 


23.6945 


0597 


16.7496 


0772 


12.9469 


35 


26 


0076 


132.219 


0250 39.9655 


0425 


23.5321 


0600 


16.6681 


0775 


12.8981 


34 


27 


0079 


127.321 


0253 395059 


0428 


23.3718 


0603 


16.5874 


0778 


12.8496 


33 


28 


0081 


122.774 


0256 390568 


0431 


23.2137 


0606 


16.5075 


0781 


12.8014 


32 


29 


0084 


118.540 


0259 38.6177 


0434 


23.0577 


0609 


16.4283 


0784 


12.7536 


31 


30 


0087 


114.589 


0262 38.1885 


0437 


22.903S 


0612 


16 3499 


0787 


12.7062 


30 


31 


0090 


110.892 


0265 37.7686 


0440 


22.7519 


0615 


16.2722 


0790 


12.6591 


29 


32 


0093 


107.426 


0268 37.3579 


0442 


22.6020 


0617 


16.1952 


0793 


12.6124 


28 


33 


0096 


104.171 


0271 36.9560 


0445 


224541 


0620 


16.1190 


0796 


12.5660 


27 


34 


0099 


101.107 


0274 36.5627 


0448 


22.30S1 


0623 


16.0435 


0799 


12.5199 


26 


35 


0102 


9S.2179 


0276 36 1776 


0451 


22.1640 


0626 


15.9687 


0802 


12.4742 


25 


36 


0105 


95.4895 


0279 35 8006 


0454 


22.0217 


"0629 


15.8945 


0805 


12.4288 


24 


37 


0108 


92.9085 


0282 35.4313 


0457 


21.8813 


0632 


15.8211 


0808 


12.3838 


23 


38 


0111 


90.4633 


0285 35.0695 


0460 


21.7426 


0635 


15.7483 


0810 


12.3390 


22 


39 


0113 


8S.1436 


02SS 34.7151 


0463 


21.6056 


063S 


15.6762 


0813 


12.2946 


21 


40 


0116 


85.939S 


0291 34.3678 


0466 


21.4704 


0641 


15.6048 


0816 


12.2505 


20 


41 


0119 


83.8435 


0294 34.0273 


0469 


21.3369 


0644 


15.5340 


0819 


12.2067 


19 


42 


0122 


81.8470 


0297 33.6935 


0472 


21.2049 


0647 


15.4638 


0822 


12.1632 


18 


43 


0125 


79 9434 


0300 33.3662 


0475 


21.0747 


0650 


15.3943 


0S25 


12.1201 


17 


44 


0128 


78.1263 


0303 33.0452 


0477 


20.9460 


0653 


15.3254 


0828 


12.0772 


16 


45 


0131 


76.3900 


0306 32.7303 


0480 


20.8188 


0655 


15.2571 


0S31 


12.0346 


15 


46 


0134 


74.7292 


0308 32.4213 


0483 


20.6932 


0658 


15.1893 


0834 


11.9923 


14 


47 


0137 


73.1390 


0311 32.1181 


0486 


20.5691 


0661 


15.1222 


0837 


11.9504 


13 


48 


0140 


71.6151 


0314 31.8205 


0489 


20.4465 


0664 


15.0557 


0840 


11.9087 


12 


49 


0143 


70.1533 


0317 31.5284 


0492 


20.3253 


0667 


14.9898 


0843 


11.8673 


11 


50 


0146 


6S.7501 


0320 31.2416 


0495 


20.2056 


0670 


14.9244 


0846 


11.8262 


10 


51 


0148 


67.4019 


0323 30.9599 


0498 


20.0S72 


0673 


14.8596 


0S49 


11.7853 


9 


52 


0151 


66.1055 


0326 30.6833 


0501 


19.9702 


0676 


14.7954 


0851 


11.7448 


8 


53 


0154 


64.85S0 


0329 30 4116 


0504 


19.8546 


0679 


14.7317 


OS54 


11.7045 


7 


54 


0157 


63.6567 


0332 301446 


0507 


19.7403 


0682 


14.6685 


0857 


11.6645 


6 


55 


0160 


62.4992 


0335 29.8823 


0509 


19.6273 


0685 


14.6059 


0860 


11.6248 


5 


56 


0163 


61.3829 


0338 29.6245 


0512 


19.5156 


0688 


14.5438 


0863 


11.5853 


4 


57 


0166 


60.3058 


0340 29.3711 


0515 


19.4051 


0690 


14.4823 


0866 


11.5461 


3 


58 


0169 


59.2659 


0343 29.1220 


0518 


19.2959 


0693 


14.4212 


0869 


11.5072 


2 


59 


0172 


5S.2612 


0346 28 8771 


0521 


19.1879 


0696 


14.3607 


0S72 


114685 


1 


60 


0175 


57.2900 


0349 28.6363 


0524 


19.0811 


0699 


14.3007 


0875 


11.4301 





r 


cot tan 
89° 


cot tan 
88° 


cot tan 
87° 


cot tan 
86° 


cot tan 
85° 




i 



62 NATURAL TANGENTS AND COTANGENTS. 



t 




5° 


6° 


7° 


8° 


9° 


t 


tan 


cot 


tan 


cot 


tan cot 


tan cot 


tan 


cot 




o 


0875 


11.4301 


1051 


9.5144 


1228 8.1443 


1405 7.1154 


1584 


6.3138 


60 


1 


0S78 


11.3919 


1054 


9.4878 


1231 8.1248 


1408 7.1004 


1587 


6.3019 


59 


2 


0SS1 


11.3540 


1057 


9.4614 


1234 S.1054 


1411 7.0855 


1590 


6.2901 


58 


3 


0SS4 


11.3163 


1060 


9.4352 


1237 8.0S60 


1414 7.0706 


1593 


6.2783 


57 


•4 


0887 


11.2789 


1063 


9.4090 


1240 8.0667 


1417 7.0558 


1596 


6.2666 


56 


5 


0890 


11.2417 


1066 


9.3831 


1243 8.0476 


1420 7.0410 


1599 


6.2549 


55 


6 


0S92 


11.2048 


1069 


9.3572 


1246 8.0285 


1423 7.0264 


1602 


6.2432 


54 


7 


0895 


11.1681 


10.72 


9.3315 


1249 8.0095 


1426 7.0117 


1605 


6.2316 


53 


8 


0898 


11.1316 


1075 


9.3060 


1251 7.9906 


1429 6.9972 


1608 


6.2200 


52 


9 


0901 


11.0954 


1078 


9.2806 


1254 7.9718 


1432 6.9827 


1611 


6.2085 


51 


10 


0904 


11.0594 


1080 


9.2553 


1257 7.9530 


1435 6.9682 


1614 


6.1970 


50 


11 


0907 


11.0237 


1083 


9.2302 


1260 7.9344 


1438 6.9538 


1617 


6.1856 


49 


12 


0910 


10.9882 


10S6 


9.2052 


1263 7.9158 


1441 6.9395 


1620 


6.1742 


48 


13 


0913 


10.9529 


1089 


9.1803 


1266 7.8973 


1444 6.9252 


1623 


6.1628 


47 


14 


0916 


10.9178 


1092 


9.1555 


1269 7.8789 


1447 6.9110 


1626 


6.1515 


46 


15 


0919 


10.8829 


1095 


9.1309 


1272 7.8606 


1450 6.8969 


1629 


6.1402 


45 


16 


0922 


10.8483 


1098 


9.1065 


1275 7.8424 


1453 6.8828 


1632 


6.1290 


44 


17 


0925 


10.8139 


1101 


9.0821 


1278 7.8243 


1456 6.8687 


1635 


6.1178 


43 


18 


0928 


10.7797 


1104 


9.0579 


1281 7.8062 


1459 6.8548 


1638 


6.1066 


42 


19 


0931 


10.7457 


1107 


9.0338 


1284 7.7883 


1462 6.8408 


1641 


6.0955 


41 


20 


0934 


10.7119 


1110 


9.0098 


1287 7.7704 


1465 6.8269 


1644 


6.0844 


40 


21 


0936 


10.6783 


1113 


8.9860 


1290 7.7525 


1468 6.8131 


1647 


6.0734 


39 


22 


0939 


10.6450 


1116 


8.9623 


1293 7.7348 


1471 67994 


1650 


6.0624 


38 


23 


0942 


10.6118 


1119 


8.9387 


1296 7.7171 


1474 6.7S56 


1653 


6.0514 


37 


24 


0945 


10.5789 


1122 


S.9152 


1299 7.6996 


1477 6.7720 


1655 


6.0405 


36 


25 


0948 


10.5462 


1125 


8 8919 


1302 7.6821 


1480 6.7584 


1658 


6.0296 


35 


26 


0951 


105136 


1128 


8.8686 


1305 7.6647 


1483 6.7448 


1661 


6.0188 


34 


27 


0954 


10.4813 


1131 


8 8455 


1308 7.6473 


1486 6.7313 


1664 


6.0080 


33 


28 


0957 


10.4491 


1134 


8.8225 


1311 7.6301 


1489 6.7179 


1667 


5.9972 


32 


29 


0960 


10.4172 


1136 


8.7996 


1314 7.6129 


1,492 6.7045 


1670 


5.9865 


31 


30 


0963 


10.3854 


1139 


8.7769 


1317 7.5958 


1495 6.6912 


1673 


5.9758 


30 


31 


0966 


10.3538 


1142 


8.7542 


1319 7.5787 


1497 6.6779 


1676 


5.9651 


29 


32 


0969 


10.3224 


1145 


8.7317 


1322 7.5618 


1500 6.6646 


1679 


5.9545 


28 


33 


0972 


10.2913 


1148 


8.7093 


1325 7.5449 


1503 6.6514 


1682 


5.9439 


27 


34 


0975 


10.2602 


1151 


8.6870 


1328 7.5281 


1506 6.6383 


1685 


5.9333 


26 


35 


0978 


10.2294 


1154 


8 6648 


1331 7.5113 


1509 6.6252 


1688 


5.9228 


25 


36 


0981 


10.1988 


1157 


8.6427* 


1334 7.4947 


1512 6.6122 


1691 


5.9124 


24 


37 


0983 


10.1683 


1160 


8.6208 


1337 7.4781 


1515 6.5992 


1694 


5.9019 


23 


38 


0986 


10.1381 


1163 


8.5989 


1340 7.4615 


1518 6.5863 


1697 


5.8915 


22 


39 


0989 


10.1080 


1166 


8.5772 


1343 7.4451 


1521 6.5734 


1700 


5.8811 


21 


40 


0992 


10.07S0 


1169 


8.5555 


1346 7.4287 


1524 6.5606 


1703 


5.8708 


20 


41 


0995 


10.0483 


. 1172 


8.5340 


1349 7.4124 


1527 6.5478 


1706 


5.8605 


19 


42 


0998 


10.0187 


1175 


8.5126 


1352 7.3962 


1530 6.5350 


1709 


5.8502 


18 


43 


1001 


9.9893 


1178 


8.4913 


1355 7.3800 


1533 6.5223 


1712 


5.8400 


17 


44 


1004 


9.9601 


1181 


8.4701 


135S 7.3639 


1536 6.5097 


1715 


5.8298 


16 


45 


1007 


9.9310 


1184 


8.4490 


1361 7.3479 


1539 6.4971 


1718 


5.8197 


15 


46 


1010 


9.9021 


1187 


8.4280 


1364 7.3319 


1542 6.4846 


1721 


5.8095 


14 


47 


1013 


9.8734 


1189 


8.4071 


1367 7.3160 


1545 6.4721 


1724 


5.7994 


13 


48 


1016 


9.8448 


1192 


8.3863' 


1370 7.3002 


1548 6.4596 


1727 


5.7894 


12 


49 


1019 


9.8164 


1195 


8.3656 


.1373 7.2844 


1551 6.4472 


1730 


5.7794 


11 


50 


1022 


9.7882 


1198 


8.3450 


1376 7.2687 


1554 6.4348 


1733 


5.7694 


10 


51 


1025 


9.7601 


1201 


8.3245 


1379 7.2531 


1557 6.4225 


1736 


5.7594 


9 


52 


1028 


9.7322 


1204 


8.3041 


. 1382 7.2375 


1560 6.4103 


1739 


5.7495 


8 


53 


1030 


9.7044 


1207 


8.2S3S 


1385 7.2220 


1563 6.3980 


1742 


5.7396 


7 


54 


1033 


9.6768 


1210 


8.2636 


.1388 7.2066 


1566 6.3SS9 


1745 


5.7297 


6 


55 


1036 


9.6499 


1213 


8.2434 


1391 7.1912 


1569 6.3737 


1748 


5.7199 


5 


56 


1039 


9 6220 


1216 


8.2234 


1394 7.1759 


1572 6.3617 


1751 


5.7101 


4 


57 


1042 


9.5949 


1219 


8.2035 


1397 7.1607 


1575 6.3496 


1754 


5.7004 


3 


5S 


1045 


9.5679 


1222 


8.1837 


1399 7.1455 


1578 6.3376 


1757 


5.6906 


2 


59 


1048 


9.5411 


1225 


8.1640 


1402 7.1304 


1581 6.3257 


1760 


5.6809 


1 


60 


1051 


9.5144 


1228 


8.1443 


1405 7.1154 


1584 6.3138 


1763 


5.6713 





r 


cot tan 
84° 


cot tan 
83° 


cot tan 

82° 


cot tan 
81° 


cot tan 
80° 




t 



NATURAL TANGENTS AND COTANGENTS. 63 



r 


10° 


11° 


12° 


13° 


14° 


t 




tan 


cot 


tan 


cot 


tan 


cot 


tan 


cot 


tan 


cot 







1763 


5.6713 


1944 


5.1446 


2126 


4.7046 


2309 


4.3315 


2493 


4.0108 


60 


1 


1766 


5.6617 


1947 


5.1366 


2129 


4.6979 


2312 


4.3257 


2496 


4.0058 


59 


2 


1769 


5.6521 


1950 


5.1286 


2132 


4.6912 


2315 


4.3200 


2499 


4.0009 


58 


3 


1772 


5.6425 


1953 


5.1207 


2135 


4.6845 


2318 


4.3143 


2503 


3.9959 


57 


4 


1775 


5.6330 


1956 


5.1128 


2138 


4.6779 


2321 


4.3086 


2506 


3.9910 


56 


5 


177S 


5.6234 


1959 


5.1049 


2141 


4.6712 


2324 


4.3029 


2509 


3.9861 


55 


6 


17S1 


5.6140 


1962 


5.0970 


2144 


4.6646 


2327 


4.2972 


2512 


3.9812 


54 


7 


17S4 


5.6045 


1965 


5.0892 


2147 


4.6580 


2330 


4.2916 


2515 


3.9763 


53 


S 


17S7 


5.5951 


1968 


5.0814 


2150 


4.6514 


2333 


4.2859 


2518 


39714 


52 


9 


1790 


5.5857 


1971 


5.0736 


2153 


4.6448 


2336 


4.2803 


2521 


3.9665 


51 


10 


1793 


5.5764 


1974 


5.065S 


2156 


4.6382 


2339 


4.2747 


2524 


3.9617 


50 


11 


1796 


5.5671 


1977 


5.0581 


2159 


4.6317 


2342 


4.2691 


2527 


3.9568 


49 


12 


1799 


5.5578 


19S0 


5.0504 


2162 


4.6252 


2345 


4.2635 


2530 


3.9520 


48 


13 


1802 


5.5485 


1983 


5 0427 


2165 


4.6187 


2349 


4.2580 


2533 


3.9471 


47 


14 


1805 


5.5393 


19S6 


5.0350 


2168 


4.6122 


2352 


4.2524 


2537 


3.9423 


46 


15 


1808 


5.5301 


1989 


5.0273 


2171 


4.6057 


2355 


4.2468 


2540 


3.9375 


45 


16 


1811 


5.5209 


1992 


5.0197 


2174 


4.5993 


2358 


4.2413 


2543 


3.9327 


44 


17 


1814 


5.5118 


1995 


5.0121 


2177 


4.5928 


2361 


4.2358 


2546 


3.9279 


43 


IS 


1817 


5.5026 


1998 


5.0045 


2180 


4.5864 


2364 


4.2303 


2549 


3.9232 


42 


19 


1820 


5.4936 


2001 


4.9969 


2183 


4.5800 


2367 


4.2248 


2552 


3.9184 


41 


20 


1823 


5.4S45 


2004 


4.9894 


2186 


4.5736 


2370 


4.2193 


2555 


3.9136 


40 


21 


1826 


5.4755 


2007 


4.9819 


2189 


4.5673 


2373 


4.2139 


2558 


3.9089 


39 


22 


1S29 


5.4665 


2010 


4.9744 


2193 


4.5609 


2376 


4.2084 


2561 


3.9042 


38 


23 


1832 


5.4575 


2013 


4.9669 


2196 


4.5546 


2379 


4.2030 


2564 


3.8995 


37 


24 


1835 


5.4486 


2016 


4.9594 


2199 


4.5483 


23S2 


4.1976 


2568 


3.8947 


36 


25 


1838 


5.4397 


2019 


4.9520 


2202 


4.5420 


2385 


4.1922 


2571 


3.8900 


35 


26 


1841 


5. 4308 


2022 


4.9446 


2205 


4.5357 


2388 


4.1868 


2574 


3.8854 


34 


27 


1844 


5.4219 


2025 


4.9372 


2208 


4.5294 


2392 


4.1814 


2577 


3.8807 


33 


28 


- 1847 


5.4131 


2028 


4.929S 


2211 


4.5232 


2395 


4.1760 


2580 


3.8760 


32 


29 


1850 


5.4043 


2031 


4.9225 


2214 


4.5169 


2398 


4.1706 


2583 


3.8714 


31 


30 


1853 


5.3955 


2035 


4.9152 


2217 


4.5107 


2401 


41653 


2586 


3.8667 


30 


31 


1856 


5.3868 


2038 


4.9078 


2220 


4.5045 


2404 


4.1600 


2589 


3.8621 


29 


32 


1859 


5.3781 


2941 


4.9006 


2223 


4.4983 


2407 


4.1547 


2592 


3.8575 


28 


33 


1862 


5.3694 


2044 


4.8933 


2226 


4.4922 


2410 


4.1493 


2595 


3.8528 


27 


34 


1865 


5.3607 


204-7 


4.8860 


2229 


4.4860 


2413 


4.1441 


2599 


3.8482 


26 


35 


186S 


5.3521 


2050 


4.S788 


2232 


4.4799 


2416 


4.1388 


2602 


3.8436 


25 


36 


1S71 


5.3435 


2053 


4.8716 


2235 


4.4737 


2419 


4.1335 


2605 


3.8391 


24 


37 


1874 


5.3349 


2056 


4.8644 


2238 


4.4676 


2422 


4.1282 


2608 


3.8345 


23 


38 


1877 


5.3263 


2059 


4.8573 


2241 


4.4615 


2425 


4.1230 


2611 


3.8299 


22 


39 


1880 


5.3178 


2062 


4.8501 


2244 


4.4555 


2428 


4.1178 


2614 


3.8254 


21 


40 


1883 


5.3093 


2065 


4.8430 


2247 


4.4494 


2432 


4.1126 


2617 


38208 


20 


41 


1887 


5.3008 


2068 


4.8359 


2251 


4.4434 


2435 


4.1074 


2620 


3.8163 


19 


42 


1890 


5.2924 


2071 


4.8288 


2254 


4.4374 


2438 


4.1022 


2623 


3.8118 


18 


43 


1893 


5.2839 


2074 


48218 


2257 


4.4313 


2441 


4.0970 


2627 


3.8073 


17 


44 


1896 


5.2755 


2077 


4.8147 


2260 


4.4253 


2444 


4.0918 


2630 


3.8028 


16 


45 


1899 


5.2672 


20S0 


4.8077 


2263 


4.4194 


2447 


40867 


2633 


3.7983 


15 


46 


1902 


5.2588 


2083 


4.8007 


2266 


4.4134 


2450 


4.0815 


2636 


3.7938 


14 


47 


1905 


5.2505 


2086 


4.7937 


2269 


4.4075 


2453 


4.0764 


2639 


3.7893 


13 


48 


1908 


5.2422 


2089 


4.7867 


2272 


4.4015 


2456 


4.0713 


2642 


3.7848 


12 


49 


1911 


5.2339 


2092 


4.7798 


2275 


4.3956 


2459 


4.0662 


2645 


3.7804 


11 


50 


1914 


5.2257 


2095 


4.7729 


2278 


4.3897 


2462 


4.0611 


2648 


3.7760 


10 


51 


1917 


5.2174 


209S 


4.7659 


2281 


4.3838 


2465 


4.0560 


2651 


3.7715 


9 


52 


1920 


5.2092' 


2101 


4.7591 


2284 


4.3779 


2469 


4.0509 


2655 


3.7671 


8 


53 


1923 


5.2011 


2104 


4.7522 


2287 


4.3721 


2472 


4.0459 


2658 


3.7627 


7 


54 


1926 


5.1929 


2107 


4.7453 


2290 


4.3662 


2475 


4.0408 


2661 


3.7583 


6 


55 


1929 


5.1848 


2110 


4.7385 


2293 


4.3604 


2478 


4.0358 


2664 


3.7539 


5 


56 


1932 


5 1767 


2113 


4.7317 


2296 


4.3546 


2481 


4.0308 


2667 


3.7495 


4 


57 


1935 


5.1686 


2116 


4.7249 


2299 


4.3488 


2484 


4 0257 


2670 


3.7451 


3 


58 


1938 


5.1606 


2119 


4.7J81 


2303 


4.3430 


2487 


4 0207 


2673 


3.7408 


2 


59 


1941 


5.1526 


2123 


4.7114 


2306 


4.3372 


2490 


4.015S 


2676 


3.7364 


1 


60 


1944 


5.1446 


2126 


4.7046 


2309 


4.3315 


2493 


4.0108 


2679 


3.7321 





t 


cot tan 
79° 


cot tan 
78° 


cot 


tan 


cot tan 
76° 


cot tan 

75° 




77° 


/ 



(34 NATURAL TANGENTS AND COTANGENTS. 



t 


15° 


16° 


17° 


18° 


19° 


r 


tan 


cot 


tan cot 


tan cot 


tan 


cot 


tan cot 





2679 


3.7321 


2S67 3.4S74 


3057 3.2709 


3249 


3.0777 


3443 2.9042 


60 


1 


26S3 


3.7277 


2871 3.4S36 


3060 3.2675 


32:^2 


3.0746 


3447 2.9015 


59 


2 


26S6 


3.7234 


2S74 3.4798 


3064 3.2641 


3256 


30716 


3450 2.8987 


58 


3 


26S9 


3.7191 


2S77 3.4760 


3067 3.2607 


3259 


3.06S6 


3453 2.S960 


57 


'4 


2692 


3.714S 


2SS0 3.4722 


3070 3.2573 


3262 


3.0655 


3456 2.S933 


56 


5 


2695 


3.7105 


2SS3 3.46S4 


3073 3.2539 


3265 


3.0625 


3460 2.S905 


55 


6 


269S 


3.7062 


2SS6 3.4646 


3076 3.2506 


3269 


3 0595 


3463 2.8878 


54 


7 


2701 


3.7019 


2S90 3.460S 


30S0 3.2472 


3272 


3.0565 


3466 2.S851 


53 


S 


2704 


3.6976 


2S93 3.4570 


30S3 3.2438 


3275 


3.0535 


3469 2.SS24 


52 


9 


270S 


3.6933 


2S96 3.4533 


30S6 3.2405 


327S 


3.0505 


3473 2.S797 


51 


10 


2711 


3.6S91 


2S99 3.4495 


30S9 3.2371 


32S1 


3.0475 


3476 2.S770 


50 


11 


2714 


3.6S4S 


2902 3.4458 


3092 3.233S 


32S5 


3 0445 


3479 2.8743 


49 


12 


2717 


3.6S06 


2905 3.4420 


3096 3.2305 


32SS 


3.0415 


3482 2.S716 


4S 


13 


2720 


3.6764 


290S 3.43S3 


3099 3.2272 


3291 


3.03S5 


3486 2.S6S9 


47 


14 


2723 


3.6722 


2912 3.4346 


3102 3.223S 


3294 


3.0356 


34S9 2.8662 


46 


15 


2726 


3.66S0 


2915 3.430S 


3105 3.2205 


329S 


3.0326 


3492 2.S636 


45 


16 


2729 


3.663S 


291S 3.4271 


310S 3.2172 


3301 


3.0296 


3495 2.8609 


44 


17 


2733 


3.6596 


2921 3.4234 


3111 3.2139 


3304 


3.0267 


3499 2.S5S2 


43 


IS 


2736 


3.6554 


2924 3.4197 


3115 3.2106 


3307 


3.0237 


3502 2.S556 


42 


19 


2739 


3.6512 


2927 3.4160 


3118 3.2073 


3310 


3.020S 


3505 2.8529 


41 


20 


2742 


3.6470 


2931 3.4124 


3121 3.2041 


3314 


3.01 7S 


3508 2.S502 


40 


21 


2745 


3.6429 


2934 3.40S7 


3124 3.200S 


3317 


3 0149 


3512 2.S476 


39 


22 


274S 


3.63S7 


2937 3.4050 


3127 3.1975 


3320 


30120 


3515 2.S449 


3S 


23 


2751 


3.6346 


2940 3.4014 


3131 3.1943 


3323 


3.0090 


35 IS 2.S423 


37 


24 


2754 


3.6305 


2943 3.3977 


3134 3.1910 


3327 


3.0061 


3522 2.S397 


36 


25 


275S 


3.6264 


2946 3.3941 


3137 3.1S7S 


3330 


3.0032 


3525 2.S370 


35 


26 


2761 


3 6222 


2949 3.3904 


3140 3.1845 


3333 


3.0003 


352S 2.S344 


34 


27 


2764 


3.61S1 


2953 3.3S6S 


3143 3.1813 


3336 


2.9974 


3531 2.S31S 


33 


2S 


2767 


3.6140 


2956 3.3S32 


3147 3.17SO 


3339 


2.9945 


3535 2.8291 


32 


29 


2770 


3.6100 


2959 3.3796 


3150 3.1748 


3343 


2 9916 


3538 2.8265 


31 


30 


2773 


3.6059 


2962 3.3759 


3153 3.1716 


3346 


2.9SS7 


3541 2.S239 


30 


31 


2776 


3.601S 


2965 3.3723 


3156 3.16S4 


3349 


2.9S5S 


3544 2.8213 


29 


32 


27S0 


3.597S 


296S 3.36S7 


3159 3.1652 


3352 


2.9S29 


354S 2.S1S7 


2S 


33 


27S3 


3.5937 


2972 3.3652 


3163 3.1620 


3356 


2.9S00 


3551 2.8161 


27 


34 


27S6 


3.5S97 


2975 3.3616 


3166 3.15SS 


3359 


2.9772 


3554 2.S135 


26 


35 


27S9 


3.5S56 


2978 3.35S0 


3169 3.1556 


3362 


2.9743 


3558 2.8109 


25 


36 


2792 


3.5S16 


29S1 3.3544 


3172 3.1524 


3365 


2.9714 


3561 2.S0S3 


24 


37 


2795 


3.5776 


29S4 3.3509 


3175 3.1492 


3369 


2.96S6 


3564 2.S057 


23 


3S 


2793 


3.5736 


2987 3.3473 


3179 3.1460 


3372 


2.9657 


3567 2.S032 


22 


39 


2S01 


3.5696 


2991 3.3438 


31S2 3.1429 


3375 


2.9629 


3571 2.S006 


21 


40 


2S05 


3.5656 


2994 3.3402 


31S5 3.1397 


337S 


2.9600 


3574 2.79S0 


20 


41 


2S0S 


3.5616 


2997 3.3367 


31SS 3.1366 


33S2 


2.9572 


3577 2.7955 


19 


42 


2S11 


3.5576 


3000 3.3332 


3191 3.1334 


33S5 


2.9544 


35S1 2.7929 


IS 


43 


2814 


3.5536 


3003 3.3297 


3195 3.1303 


33SS 


2.9515 


3584 2.7903 


17 


44 


2S17 


3.5497 


3006 3.3261 


319S 3.1271 


3391 


2.94S7 


35S7 2.7S7S 


16 


45 


2S20 


3.5457 


3010 3.3226 


3201 3.1240 


3395 


2.9459 


3590 2.7S52 


15 


46 


2S23 


3.541S 


3013 3.3191 


3204 3.1209 


339S 


2.9431 


3594 2.7827 


14 


47 


2S27 


3.5379 


3016 3.3156 


3207 3.1178 


3401 


2.9403 


3597 2.7801 


13 


4S 


2S30 


3.5339 


3019 3.3122 


3211 3.1146 


3404 


2.9375 


3600 2.7776 


12 


49 


2S33 


3.5300 


3022 3.30S7 


3214 3.1115 


340S 


2.9347 


3604 2.7751 


11 


50 


2S36 


3.5261 


3026 3.3052 


3217 3.10S4 


3411 


2.9319 


3607 2.7725 


10 


51 


2S39 


3.5222 


3029 3.3017 


3220 3.1053 


3414 


2.9291 


3610 2.7700 


9 


52 


2S42 


3.5183 


3032 3.29S3 


3223 3.1022 


3417 


2.9263 


3613 2.7675 


8 


53 


2845 


3.5144 


3035 3.294S 


3227 3.0991 


3421 


2.9235 


3617 2.7650 


7 


54 


2849 


3.5105 


303S 3.2914 


3230 3.0961 


3424 


2.920S 


3620 2.7625 


6 


55 


2S52 


3.5067 


3041 3.2SS0 


3233 3.0930 


3427 


2.91S0 


3623 2.7600 


5 


56 


2855 


3 502S 


3045 3.2S45 


3236 3.0S99 


3430 


2.9152 


3627 2.7575 


4 


57 


2S5S 


3.49S9 


304S 3.2S11 


3240 3.0S6S 


3434 


2.9125 


3630 2.7550 


3 


58 


2S61 


3.4951 


3051 3.2777 


3243 3.0S3S 


3437 


2.9097 


3633 2.7525 


2 


59 


2S64 


3.4912 


3054 3.2743 


3246 3.0S07 


3440 


2.9070 


3636 2 7500 


1 


60 


2867 


3.4S74 


3057 3.2709 


3249 3.0777 


3443 


2.9042 


3640 2.7475 







cot 


tan 


cot tan 


cot tan 


cot 


tan 


cot tan 




t 


7 


4° 


73° 


72° 


7 


1° 


70° 


t 



NATURAL TANGENTS AND COTANGENTS. 65 



t 


20° 


21° 


22° 


23° 


24° 


t 




tan 


cot 


tan cot 


tan 


cot 


tan 


cot 


tan 


cot 







3640 


2.7475 


3839 2.6051 


4040 


2.4751 


4245 


2.3559 


4452 


2.2460 


60 


1 


3643 


2.7450 


3842 2.6028 


4044 


2.4730 


4248 


2.3539 


4456 


2.2443 


59 


2 


3646 


2.7425 


3845 2.6006 


4047 


2.4709 


4252 


2.3520 


4459 


2.2425 


58 


3 


3650 


2.7400 


3849 2.5983 


4050 


2.46S9 


4255 


2.3501 


4463 


2.240S 


57 


4 


3653 


2.7376 


3852 2.5961 


4054 


2.4668 


4258 


2.3483 


4466 


2.2390 


56 


5 


3656 


2.7351 


3855 2.593S 


4057 


2.4648 


4262 


2.3464 


4470 


2.2373 


55 


6 


3659 


2.7326 


3859 2.5916 


4061 


2.4627 


4265 


2.3445 


4473 


2.2355 


54 


1 7 


3663 


2.7302 


3862 2.5893 


4064 


2.4606 


4269 


2.3426 


4477 


2.2338 


53 


8 


3666 


2.7277 


3865 2.5871 


4067 


2.4586 


4272 


2.3407 


4480 


2.2320 


52 


9 


3669 


2.7253 


3869 2.584S 


4071 


2.4566 


4276 


2.3388 


4484 


2.2303 


51 


10 


3673 


2.722S 


3872 2.5826 


4074 


2.4545 


4279 


2.3369 


4487 


2.2286 


50 


11 


3676 


2.7204 


3875 2.5804 


407S 


2.4525 


4283 


2.3351 


4491 


2.2268 


49 


12 


3679 


2.7179 


3879 2.57S2 


4081 


2.4504 


4286 


2.3332 


4494 


2.2251 


48 


13 


3683 


2.7155 


38S2 2.5759 


4084 


2.4484 


4289 


2.3313 


4498 


2.2234 


47 


14 


3686 


2.7130 


3885 2.5737 


40SS 


2.4464 


4293 


2.3294 


4501 


2.2216 


46 


15 


3689 


2.7106 


3889 2.5715 


4091 


2.4443 


4296 


2.3276 


4505 


2.2199 


45 


16 


3693 


2.7082 


3892 2.5693 


4095 


2.4423 


4300 


2.3257 


450S 


2.2182 


44 


17 


3696 


2.7058 


3S95 2.5671 


4098 


2.4403 


4303 


2.3238 


4512 


2.2165 


43 


IS 


3699 


2.7034 


3899 2.5649 


4101 


2.4383 


4307 


2.3220 


4515 


2.2148 


42 


19 


3702 


2.7009 


3902 2.5627 


4105 


2.4362 


4310 


2.3201 


4519 


2.2130 


41 


20 


3706 


2.69S5' 


3906 2.5605 


4108 


2.4342 


4314 


2.3183 


4522 


2.2113 


40 


21 


3709 


2.6961 


3909 2.5533 


4111 


2.4322 


4317 


2.3164 


4526 


2.2096 


39 


22 


3712 


2.6937 


3912 2.5561 


4115 


2.4302 


4320 


2.3146 


4529 


2.2079 


38 


23 


3716 


2.6913 


3916 2.5539 


4118 


2.4282 


4324 


2.3127 


4533 


2.2062 


37 


24 


3719 


2.6SS9 


3919 2.5517 


4122 


2.4262 


4327 


2.3109 


4536 


2.2045 


36 


25 


3722 


2.6865 


3922 2.5495 


4125 


2.4242 


4331 


2.3090 


4540 


2.2028 


35 


26 


3726 


2.6841 


3926 2.5473 


4129 


2.4222 


4334 


2.3072 


4543 


2.2011 


34 


27 


3729 


2.6S18 


3929 2.5452 


4132 


2.4202 


4338 


2.3053 


4547 


2.1994 


33 


2S 


3732 


2.6794 


3932 2.5430 


4135 


2.4182 


4341 


2.3035 


4550 


2.1977 


32 


29 


3736 


2.6770 


3936 2.5408 


4139 


2.4162 


4345 


2.3017 


4554 


2.1960 


31 


30 


3739 


2.6746 


3939 2.5386 


4142 


2.4142 


4348 


2.2998 


4557 


2.1943 


30 


31 


3742 


2.6723 


3942 2.5365 


4146 


2.4122 


4352 


2.2980 


4561 


2.1926 


29 


32 


3745 


2.6699 


3946 2.5343 


4149 


2.4102 


4355 


2.2962 


4564 


2.1909 


28 


33 


3749 


2.6675 


3949 2.5322 


4152 


2.4083 


4359 


2.2944 


4568 


2.1892 


27 


34 


3752 


2.6652 


3953 2.5300 


4156 


2.4063 


4362 


2.2925 


4571 


2.1876 


26 


35 


3755 


2.6628 


3956 2.5279 


4159 


2.4043 


4365 


2.2907 


4575 


2.1859 


25 


36 


3759 


2.6605 


3959 2.5257 


4163 


2.4023 


4369 


2.2889 


4578 


2.1842 


24 


37 


3762 


2.6581 


3963 2.5236 


4166 


2.4004 


4372 


2.2871 


4582 


2.1825 


23 


38 


3765 


2.6558 


3966 2.5214 


4169 


2.3984 


4376 


2.2853 


4585 


2.1808 


22 


39 


3769 


2.6534 


3969 2.5193 


4173 


2.3964 


4379 


2.2835 


4589 


2.1792 


21 


40 


3772 


2.6511 


3973 2.5172 


4176 


2.3945 


4383 


2.2817 


4592 


2.1775 


20 


41 


3775 


2.6488 


3976 2.5150 


41S0 


2.3925 


4386 


2.2799 


4596 


2.1758 


19 


42 


3779 


2.6464 


3979 2.5129 


4183 


2.3906 


4390 


22781 


4599 


2.1742 


IS 


43 


3782 


2.6441 


3983 2 5108 


4187 


2.3886 


4393 


2.2763 


4603 


2.1725 


17 


44 


3785 


2.6418 


3986 2.5086 


4190 


2.3867 


4397 


2.2745 


4607 


2.1708 


16 


45 


3789 


2.6395 


3990 2.5065 


4193 


2.3847 


4400 


2.2727 


4610 


2.1692 


15 


46 


3792 


2.6371 


3993 2.5044 


4197 


2.3828 


4404 


2.2709 


4614 


2.1675 


14 


47 


3795 


2.6348 


3996 2.5023 


4200 


2.3808 


4407 


2.2691 


4617 


2.1659 


13 


48 


3799 


2.6325 


4000 2.5002 


4204 


2.3789 


4411 


2.2673 


4621 


2.1642 


12 


49 


3802 


2.6302 


4003 2.4981 


4207 


2.3770 


4414 


2.2655 


4624 


2.1625 


11 


50 


3805 


2.6279 


4006 2.4960 


4210 


2.3750 


4417 


2.2637 


4628 


2.1609 


io 


51 


3809 


2.6256 


4010 2.4939 


4214 


2.3731 


4421 


2.2620 


4631 


2.1592 


9 


52 


3812 


2.6233 ■ 


4013 2.4918 


4217 


2.3712 


4424 


2.2602 


4635 


2.1576 


8 


53 


3815 


2.6210 


4017 2.4897 


4221 


2.3693 


4428 


2.2584 


4638 


2.1560 


7 


54 


3819 


2.6187 


4020 2.4876 


4224 


2.3673 


4431 


2.2566 


4642 


2.1543 


6 


55 


3822 


2.6165 


4023 2.4855 


4228 


2.3654 


4435 


2.2549 


4645 


2.1527 


5 


56 


3825 


2 6142 


4027 2.4834 


4231 


2.3635 


4438 


2.2531 


4649 


2.1510 


4 


57 


3829 


2.6119 


4030 2.4813 


4234 


2.3616 


4442 


2.2513 


4652 


2.1494 


3 


58 


3832 


26096 


4033 2.4792 


423S 


2.3597 


4445 


2.2496 


4656 


2.1478 


2 


59 


3835 


2.6074 


4037 2.4772 


4241 


2.357S 


4449 


2.2478 


4660 


2.1461 


1 


60 


3839 


2.6051 


4040 2.4751 


4245 


2.3559 


4452 


2.2460 


4663 


2.1445 





t 


cot tan 
69° 


cot tan 
68° 


cot tan 
67° 


cot tan 
66° 


cot tan 
65° 




t 



66 NATURAL TANGENTS AND COTANGENTS. 



f 


25° 


26° 


27° 


28° 


29° 


r 


tan 


cot 


tan 


cot 


tan cot 


tan 


cot 


tan 


cot 





46b3 


2.1445 


4877 


2.0503 


5095 1.9626 


5317 


1.8807 


5543 


1.8040 


60 


1 


4b67 


2.1429 


4881 


2.0488 


5099 1.9612 


5321 


1.8794 


5547 


1.802S 


59 


2 


4670 


2.1413 


4885 


2.0473 


5103 1.9598 


5325 


1.S781 


5551 


1.8016 


58 


3 


4674 


2.1396 


4888 


2.0458 


5106 1.95S4 


532S 


1.8768 


5555 


1.8003 


57 


4 


4677 


2.1380 


4892 


2.0443 


5110 1.9570 


5332 


1.8755 


5558 


1.7991 


56 


5 


4681 


2.1364 


4895 


2.0428 


5114 1.9556 


5336 


1.S741 


5562 


1.7979 


55 


6 


4684 


2.1348 


4899 


2.0413 


5117 1.9542 


5340 


1.8728 


5566 


1.7966 


54 


7 


46S8 


2.1332 


4903 


2.0398 


5121 1.9528 


5343 


1.S715 


5570 


1.7954 


53 


8 


4691 


2.1315 


4906 


2.0383 


5125 1.9514 


5347 


1.8702 


5574 


1.7942 


52 


9 


4695 


2.1299 


4910 


2.0368 


512S 1.9500 


5351 


1.8689 


5577 


1.7930 


51 


10 


4699 


2.1283 


4913 


2.0353 


5132 1.9486 


5354 


1.8676 


5581 


1.7917 


50 


11 


4702 


2.1267 


4917 


2.033S 


5136 1.9472 


5358 


1.S663 


5585 


1.7905 


49 


12 


4706 


2.1251 


4921 


2.0323 


5139 1.9458 


5362 


1.8650 


5589 


1.7893 


48 


13 


4709 


2.1235 


4924 


2 0308 


5143 1.9444 


5366 


1.8637 


5593 


1.7881 


47 


14 


4713 


2.1219 


4928 


2.0293 


5147 1.9430 


5369 


1.8624 


5596 


1.7868 


46 


15 


4716 


2.1203 


4931 


2.0278 


5150 1.9416 


5373 


.1.8611 


5600 


1.7856 


45 


16 


4720 


2.1187 


4935 


2.0263 


5154 1.9402 


5377 


1.8598 


5604 


1.7844 


44 


17 


4723 


2.1171 


4939 


2.024S 


5158 1.9388 


5381 


1.8585 


560S 


1.7832 


43 


IS 


4727 


2.1155 


4942 


2.0233 


5161 1.9375 


5384 


1.S572 


5612 


1.7820 


42 


19 


4731 


2.1139 


4946 


2.0219 


5165 1.9361 


5388 


1.8559 


5616 


1.7808 


41 


20 


4734 


2.1123 


4950 


2.0204 


5169 1.9347 


5392 


1.8546 


5619 


1.7796 


40 


21 


4738 


2.1107 


4953 


2.0189 


5172 1.9333 


5396 


1.8533 


5623 


1.7783 


39 


22 


4741 


2.1092 


4957 


2.0174 


5176 1.9319 


5399 


1.8520 


5627 


1.7771 


38 


23 


4745 


2.1076 


4960 


2.0160 


5180 1.9306 


5403 


1.8507 


5631 


1.7759 


37 


24 


4748 


2.1060 


4964 


2.0145 


5184 1.9292 


5407 


1.8495 


5635 


1.7747 


36 


25 


4752 


2.1044 


496S 


20130 


5187 1.9278 


5411 


1.8482 


5639 


1.7735 


35 


26 


4755 


2 1028 


4971 


2.0115 


5191 1.9265 


5415 


1.8469 


5642 


1.7723 


34 


27 


4759 


2.1013 


4975 


2 0101 


5195 1.9251 


5418 


1.8456 


5646 


1.7711 


33 


2S 


4763 


2.0997 


4979 


2.0086 


5198 1.9237 


5422 


1.8443 


5650 


1.7699 


32 


29 


4766 


2.0981 


4982 


2.0072 


5202 1.9223 


.5426 


18430 


5654 


1.7687 


31 


30 


4770 


2.0965 


4986 


2.0057 


5206 1.9210 


5430 


1.8418 


5658 


1.7675 


30 


31 


4773 


2.0950 


49S9 


2.0042 


5209 1.9196 


5433 


1.8405 


5662 


1.7663 


29 


32 


4777 


2.0934 


4993 


2.002S 


5213 1.9183 


5437 


1.8392 


5665 


1.7651 


28 


33 


4780 


2.0918 


4997 


2.0013 


5217 1.9169 


5441 


1.8379 


5669 


1.7639 


27 


34 


4784 


2.0903 


5000 


1.9999 


5220 1.9155 


5445 


1.8367 


5673 


1.7627 


26 


35 


4788 


2.0887 


5004 


1.9984 


5224 1.9142 


5448 


1.8354 


5677 


1.7615 


25 


36 


4791 


2.0872 


5008 


1.9970 


5228 1.9128 


5452 


1.8341 


5681 


1.7603 


24 


37 


4795 


2.0856 


5011 


1.9955 


5232 1.9115 


5456 


1.8329 


5685 


1.7591 


23 


38 


4798 


2.0840 


5015 


1.9941 


5235 1.9101 


5460 


1.8316 


5688 


1.7579 


22 


39 


4802 


2.0825 


5019 


1.9926 


5239 1.9088 


5464 


1.8303 


5692 


1.7567 


21 


40 


4806 


2.0809 


5022 


1.9912 


5243 1.9074 


5467 


1.8291 


5696 


1.7556 


20 


41 


4809 


2.0794 


5026 


1.9897 


5246 1.9061 


5471 


1.S278 


5700 


1.7544 


19 


42 


4813 


2.0778 


5029 


1.9883 


5250 1.9047 


5475 


1.S265 


5704 


1.7532 


18 


43 


4816 


2.0763 


5033 


1.9868 


5254 1.9034 


5479 


1.8253 


5708 


1.7520 


17 


44 


4820 


2.0748 


5037 


1.9854 


5258 . 1.9020 


5482 


1.8240 


5712 


1.7508 


16 


45 


4823 


2.0732 


5040 


1.9840 


5261 1.9007 


5486 


1.8228 


5715 


1.7496 


15 


46 


4827 


2.0717 


5044 


1.9825 


5265 1.8993 


5490 


1.8215 


5719 


1.7485 


14 


47 


4831 


2.0701 


5048 


1.9811 


5269 ' 1.8980 


5494 


1.8202 


5723 


1.7473 


13 


48 


4834 


2.0686 


5051 


1.9797 


5272 1.8967 


5498 


1.8190 


5727 


1.7461 


12 


49 


4838 


2.0671 


5055 


1.9782 


5276 1.8953 


5501 


1.8177 


5731 


1.7449 


11 


50 


4841 


2.0655 


5059 


1.976S 


5280 1.8940 


5505 


1.8165 


5735 


1.7437 


10 


51 


4845 


2.0640 


5062 


1.9754 


5284 1.8927 


5509 


1.S152 


5739 


1.7426 


9 


52 


4849 


2.0625 


5066 


1.9740 


5287 1.8913 


5513 


1.8140 


5743 


1.7414 


8 


53 


4S52 


2.0609 


5070 


1.9725 


5291 1.8900 


5517 


1.8127 


5746 


1.7402 


7 


54 


4856 


2.0594 


5073 


1.9711 


5295 1.8887 


5520 


1.8115 


5750 


1.7391 


6 


55 


4859 


2.0579 


5077 


1.9697 


5298 1.8873 


5524 


1.8103 


5754 


1.7379 


5 


56 


4863 


2 0564 


5081 


1.9683 


5302 1.8860 


5528 


1.8090 


575S 


1.7367 


4 


57 


4867 


2.0549 


5084 


1.9669 


5306 1.8847 


5532 


1.8078 


5762 


1.7355 


3 


5S 


4870 


2 0533 


5088 


1.9654 


5310 1.8834 


5535 


1.8065 


5766 


1.7344 


2 


59 


4874 


2.0518 


5092 


1.9640 


5313 1.8S20 


5539 


1.8053 


5770 


1.7332 


1 


60 


4877 


2.0503 


5095 


1.9626 


5317 1.8807 


5543 


1.8040 


5774 


1.7321 





t 


cot tan 
64° 


cot tan 
63° 


cot tan 

62° 


cot tan 
61° 


cot tan 
60° 




t 



NATURAL TANGENTS AND COTANGENTS. 67 



t 


30° 


31° 


32° 


33° 


34° 


t 


tan 


cot 


tan 


cot 


tan 


cot 


tan 


cot 


tan 


cot 





5774 


1.7321 


6009 


1.6643 


6249 


1.6003 


6494 


1.5399 


6745 


1.4826 


60 


1 


5777 


1.7309 


6013 


1.6632 


6253 


1.5993 


649S 


1.53S9 


6749 


1.4S16 


59 


2 


5781 


1.7297 


6017 


1.6621 


6257 


1.59S3 


6502 


1.5379 


6754 


1.4807 


58 


3 


5785 


1.72S6 


6020 


1.6610 


6261 


1.5972 


6506 


1.5369 


6758 


1.479S 


57 


4 


5789 


1.7274 


6024 


1.6599 


6265 


1.5962 


6511 


1.5359 


6762 


1.4788 


56 


5 


5793 


1.7262 


6028 


1.65SS 


6269 


1.5952 


6515 


1.5350 


6766 


1.4779 


55 


6 


5797 


1.7251 


6032 


1.6577 


6273 


1.5941 


6519 


1.5340 


6771 


1.4770 


54 


7 


5801 


1.7239 


6036 


1.6566 


6277 


1.5931 


6523 


1.5330 


6775 


1.4761 


53 


8 


5S05 


1.722S 


6040 


1.6555 


6281 


1.5921 


6527 


1.5320 


6779 


1.4751 


52 


9 


'5808 


1.7216 


6044 


1.6545 


62S5 


1.5911 


6531 


1.5311 


6783 


1.4742 


51 


10 


5812 


1.7205 


6048 


1.6534 


6289 


1.5900 


6536 


1.5301 


6787 


1.4733 


50 


11 


5816 


1.7193 


6052 


1.6523 


6293 


1.5890 


6540 


1.5291 


6792 


1.4724 


49 


12 


5820 


1.7182 


6056 


1.6512 


6297 


1.5880 


6544 


1.5282 


6796 


1.4715 


48 


13 


5824 


1.7170 


6060 


16501 


6301 


1.5S69 


6548 


1.5272 


6800 


1.4705 


47 


14 


5828 


1.7159 


6064 


1.6490 


6305 


1.5859 


6552 


1.5262 


6805 


1.4696 


46 


15 


5832 


1.7147 


6068 


1.6479 


6310 


1.5849 


6556 


1.5253 


6809 


1.4687 


45 


16 


5836 


1.7136 


6072 


1.6469 


6314 


1.5S39 


6560 


1.5243 


6813 


1.467S 


44 


17 


5840 


1.7124 


6076 


1.645S 


6318 


1.5829 


6565 


1.5233 


6S17 


1.4669 


43 


18 


5S44 


1.7113 


6080 


1.6447 


6322 


1.5S1S 


6569 


1.5224 


6822 


1.4659 


42 


19 


5S47 


1.7102 


6084 


1.6436 


6326 


1.5808 


6573 


1.5214 


6826 


1.4650 


41 


20 


5851 


1.7090 


60SS 


1.6426 


6330 


1.579S 


6577 


1.5204 


6830 


1.4641 


40 


21 


5855 


1.7079 


6092 


1.6415 


6334 


1.5788 


6581 


1.5195 


6S34 


1.4632 


39 


22 


5859 


1.7067 


6096 


1.6404 


633S 


1.577S 


6585 


1.5185 


6839 


1.4623 


38 


23 


5863 


1.7056 


6100 


1.6393 


6342 


1.576S 


6590 


1.5175 


6S43 


1.4614 


37 


24 


5867 


1.7045 


6104 


1.6383 


6346 


1.5757 


6594 


1.5166 


6847 


1.4605 


36 


25 


5871 


1.7033 


6108 


1.6372 


6350 


1.5747 


659S 


1.5156 


6851 


1.4596 


35 


26 


5875 


1.7022 


6112 


1.6361 


6354 


1.5737 


6602 


1.5147 


6S56 


1.45S6 


34 


27 


5879 


1.7011 


6116 


1.6351 


6358 


1.5727 


6606 


1.5137 


6860 


1.4577 


33 


28 


5883 


1.6999 


6120 


1.6340 


6363 


1.5717 


6610 


1.5127 


6864 


1.4568 


32 


29 


5SS7 


1.69SS 


6124 


1.6329 


' 6367 


1.5707 


6615 


1.5118 


6S69 


1.4559 


31 


30 


5890 


1.6977 


6128 


1.6319 


6371 


1.5697 


6619 


1.5108 


6873 


1.4550 


30 


31 


5894 


1.6965 


6132 


1.6308 


6375 


1.5687 


6623 


1.5099 


6877 


1.4541 


29 


32 


5S9S 


1.6954 


6136 


1.6297 


6379 


1.5677 


6627 


1.5089 


6SS1 


1.4532 


28 


33 


5902 


1.6943 


6140 


1.6287 


6383 


1.5667 


6631 


1.5080 


6886 


1.4523 


27 


34 


5906 


1.6932 


6144 


1.6276 


63S7 


1.5657 


6636 


1.5070 


6S90 


1.4514 


26 


35 


5910 


1.6920 


6148 


1.6265 


6391 


1.5647 


6640 


1.5061 


6894 


1.4505 


25 


36 


5914 


1.6909 


6152 


16255 


6395 


1.5637 


6644 


1.5051 


6899 


1.4496 


24 


37 


5918 


1.6S9S 


6156 


1.6244 


6399 


1.5627 


6648 


1.5042 


6903 


1.4487 


23 


3S 


5922 


1.6S87 


6160 


1.6234 


6403 


1.5617 


6652 


1.5032 


6907 


1.4478 


22 


39 


5926 


1.6875 


6164 


1.6223 


6408 


1.5607 


6657 


1.5023 


6911 


1.4469 


21 


40 


5930 


1.6S64 


6168 


1.6212 


6412 


1.5597 


6661 


1.5013 


6916 


1.4460 


20 


41 


5934 


1.6853 


6172 


1.6202 


6416 


1.5587 


6665 


1.5004 


6920 


1.4451 


19 


42 


5938 


1.6842 


6176 


1.6191 


6420 


1.5577 


6669 


1.4994 


6924 


1.4442 


18 


43 


5942 


1.6831 


61S0 


1.6181 


6424 


1.5567 


6673 


1.4985 


6929 


1.4433 


17 


44 


5945 


1.6820 


6184 


1.6170 


6428 


1.5557 


6678 


1.4975 


6933 


1.4424 


16 


45 


5949 


1.6S0S 


61SS 


1.6160 


6432 


1.5547 


6682 


1.4966 


6937 


1.4415 


15 


46 


5953 


1.6797 


6192 


1.6149 


6436 


1.5537 


6686 


1.4957 


6942 


1.4406 


14 


47 


5957 


1.6786 


6196 


1.6139 


6440 


1.5527 


6690 


1.4947 


6946 


1.4397 


13 


48 


5961 


1.6775 


6200 


1.6128 


6445 


1.5517 


6694 


1.4938 


6950 


1.4388 


12 


49 


5965 


1.6764 


6204 


1.6118 


6449 


1.5507 


6699 


1.4928 


6954 


1.4379 


11 


50 


5969 


1.6753 


620S 


1.6107 


6453 


1.5497 


6703 


1.4919 


6959 


1.4370 


io 


51 


5973 


1.6742 


6212 


1.6097 


6457 


1.54S7 


6707 


1.4910 


6963 


1.4361 


9 


52 


5977 


1.6731 


6216 


1.6087 


6461 


1.5477 


6711 


1.4900 


6967 


1.4352 


8 


53 


5981 


1.6720 


6220 


1.6076 


6465 


1.5468 


6716 


1.4891 


6972 


1.4344 


7 


54 


5985 


1.6709 


6224 


1.6066 


6469 


1.5458 


6720 


1.4SS2 


6976 


1.4335 


6 


55 


5989 


1.6698 


6228 


1.6055 


6473 


1.5448 


6724 


1.4872 


69S0 


1.4326 


5 


56 


5993 


166S7 


6233 


1.6045 


6478 


1.543S 


672S 


1.4863 


69S5 


1.4317 


4 


57 


5997 


1.6676 


6237 


1.6034 


6482 


1.5428 


6732 


1.4854 


6989 


1.4308 


3 


58 


6001 


16665 


6241 


1.6024 


64S6 


1.5418 


6737 


1.4844 


6993 


1.4299 


2 


59 


6005 


1.6654 


6245 


1.6014 


6490 


1.5408 


6741 


1.4835 


6998 


1.4290 


1 


60 


6009 


1.6643 


6249 


1.6003 


6494 


1.5399 


6745 


1.4826 


7002 


1.4281 





t 


cot tan 
59° 


cot tan 
58° 


cot tan 

57° 


cot tan 
56° 


cot tan 

55° 




t 



NATURAL TANGENTS AND COTANGENTS. 



t 


35° 


36° 


37° 


38° 


39° 


t 


tan 


cot 


tan 


cot 


tan 


cot 


tan 


cot 


tan 


cot 







7002 


14281 


7265 


1.3764 


7536 


1.3270 


7813 


1.2799 


8098 


1.2349 


60 


1 


7006 


1.4273 


7270 


1.3755 


7540 


1.3262 


7818 


1.2792 


8103 


1.2342 


59 


2 


7011 


1.4264 


7274 


1.3747 


7545 


1.3254 


7822 


1.2784 


8107 


1.2334 


58 


3 


7015 


1.4255 


7279 


1.3739 


7549 


1.3246 


7827 


1.2776 


8112 


1.2327 


57 


4 


7019 


1.4246 


7283 


1.3730 


7554 


1.3238 


7832 


1.2769 


8117 


1.2320 


56 


5 


7024 


1.4237 


7288 


1.3722 


7558 


1.3230 


7836 


1.2761 


8122 


1.2312 


55 


6 


7028 


1.4229 


7292 


1.3713 


7563 


1.3222 


7841 


1.2753 


8127 


1.2305 


54 


7 


7032 


1.4220 


7297 


1.3705 


7568 


1.3214 


7846 


1.2746 


8132 


1.2298 


53 


8 


7037 


1.4211 


7301 


1.3697 


7572 


1.3206 


7850 


1.2738 


8136 


1.2290 


52 


9 


7041 


1.4202 


7306 


1.3688 


7577 


1.3198 


7855 


1.2731 


8141 


1.2283 


51 


io 


7046 


1.4193 


7310 


1.3680 


7581 


1.3190 


7860 


1.2723 


8146 


1.2276 


50 


11 


7050 


1.4185 


7314 


1.3672 


7586 


1.3182 


7865 


1.2715 


8151 


1.2268 


49 


12 


7054 


1.4176 


7319 


1.3663 


7590 


1.3175 


7869 


1.2708 


8156 


1.2261 


48 


13 


7059 


1.4167 


7323 


1.3655 


7595 


1.3167 


7874 


1.2700 


8161 


1.2254 


47 


14 


7063 


1.4158 


7328 


1.3647 


7600 


1.3159 


7879 


1.2693 


8165 


1.2247 


46 


15 


7067 


1.4150 


7332 


1.3638 


7604 


1.3151 


7883 


12685 


8170 


1.2239 


45 


16 


7072 


1.4141 


7337 


1.3630 


7609 


1.3143 


7888 


1.2677 


8175 


1.2232 


44 


17 


7076 


1.4132 


7341 


1.3622 


7613 


1.3135 


7893 


1.2670 


8180 


1.2225 


43 


IS 


7080 


1.4124 


7346 


1.3613 


7618 


1.3127 


7898 


1.2662 


8185 


1.2218 


42 


19 


7085 


1.4115 


7350 


1.3605 


7623 


1.3119 


7902 


1.2655 


8190 


1.2210 


41 


20 


7089 


1.4106 


7355 


1.3597 


7627 


1.3111 


7907 


1.2647 


8195 


1.2203 


40 


21 


7094 


1.4097 


7359 


1.3588 


7632 


1.3103 


7912 


1.2640 


8199 


1.2196 


39 


22 


7098 


1.4089 


7364 


1.3580 


7636 


1.3095 


7916 


1.2632 


8204 


1.2189 


38 


23 


7102 


1.4080 


7368 


1.3572 


7641 


1.3087 


7921 


1.2624 


8209 


1.2181 


37 


24 


7107 


1.4071 


7373 


1.3564 


7646 


1.3079 


7926 


1.2617 


8214 


1.2174 


36 


25 


7111 


1.4063 


7377 


1.3555 


7650 


1.3072 


7931 


1.2609 


8219 


1.2167 


35 


26 


. 7115 


1.4054 


7382 


1.3547 


7655 


1.3064 


7935 


1.2602 


8224 


1.2160 


34 


27 


7120 


1.4045 


7386 


1.3539 


7659 


1.3056 


7940 


1.2594 


8229 


1.2153 


33 


28 


7124 


1.4037 


7391 


1.3531 


7664 


1.3048 


7945 


1.2587 


8234 


1.2145 


31 


29 


7129 


1.4028 


7395 


1.3522 


7669 


1.3040 


7950 


1.2579 


8238 


1.2138 


31 


30 


7133 


1.4019 


7400 


1.3514 


7673 


1.3032 


7954 


1.2572 


8243 


1.2131 


30 


31 


7137 


14011 


7404 


1.3506 


7678 


1.3024 


7959 


1.2564 


8248 


1.2124 


29 


32 


7142 


1.4002 


7409 


1.3498 


7683 


1.3017 


7964 


1.2557 


8253 


1.2117 


28 


33 


7146 


1.3994 


7413 


1.3490 


7687 


1.3009 


7969 


1.2549 


8258 


1.2109 


27 


34 


7151 


1.3985 


7418 


1.3481 


7692 


1.3001 


7973 


1.2542 


8263 


1.2102 


26 


35 


7155 


1.3976 


7422 


1.3473 


7696 


1.2993 


7978 


1.2534 


8268 


1.2095 


25 


36 


7159 


1.3968 


7427 


1.3465 


7701 


1.2985 


7983 


1.2527 


8273 


1.2088 


24 


37 


7164 


1.3959 


7431 


1.3457 


7706 


1.2977 


7988 


1.2519 


8278 


1.2081 


23 


38 


716S 


1.3951 


7436 


1.3449 


7710 


1.2970 


7992 


1.2512 


8283 


1.2074 


22 


39 


7173 


1.3942 


7440 


1.3440 


7715 


1.2962 


7997 


1.2504 


8287 


1.2066 


21 


40 


7177 


1.3934 


7445 


1.3432 


7720 


1.2954 


8002 


1.2497 


8292 


1.2059 


20 


41 


7181 


1.3925 


7449 


1.3424 


7724 


1.2946 


8007 


1.2489 


8297 


1.2052 


19 


42 


7186 


1.3916 


7454 


1.3416 


7729 


1.2938 


8012 


1.2482 


8302 


1.2045 


18 


43 


7190 


1.3908 


7458 


1.3408 


7734 


1.2931 


8016 


1.2475 


8307 


1.2038 


17 


44 


7195 


1.3S99 


7463 


1.3400 


7738 


1,2923 


8021 


1.2467 


8312 


1.2031 


16 


45 


7199 


1.3891 


7467 


1.3392 


7743 


1.2915 


8026 


1.2460 


8317 


1.2024 


15 


46 


7203 


1.3882 


7472 


1.3384 


7747 


1.2907 


8031 


1.2452 


8322 


1.2017 


14 


47 


7208 


1.3874 


7476 


1.3375 


-7752 


1.2900 


8035 


1.2445 


8327 


12009 


13 


4S 


7212 


1.3865 


7481 


1.3367 


7757 


1.2892 


8040 


1.2437 


8332 


1.2002 


12 


49 


7217 


1.3857 


7485 


1.3359 


7761 


1.2S84 


8045 


1.2430 


8337 


1.1995 


11 


50 


7221 


1.3848 


7490 


1.3351 


7766 


1.2876 


8050 


1.2423 


8342 


1.1988 


10 


51 


7226 


1.3840 


7495 


1.3343 


7771 


1.2869 


8055 


1.2415 


8346 


1.1981 


9 


52 


7230 


1.3831 


7499 


1.3335 


7775 


1.2861 


8059 


1.2408 


8351 


1.1974 


8 


53 


7234 


1.3823 


7504 


1.3327 


77S0 


1.2853 


8064 


1.2401 


8356 


1.1967 


7 


54 


7S39 


1.3814 


7508 


1.3319 


7785 


1.2846 


8069 


1.2393 


8361 


1.1960 


6 


55 


7243 


1.3806 


7513 


1.3311 


7789 


1.2838 


8074 


1.2386 


8366 


1.1953 


5 


56 


7248 


1.3798 


7517 


1.3303 


7794 


1.2S30 


8079 


1.2378 


8371 


1.1946 


4 


57 


7252 


1.3789 


7522 


1.3295 


7799 


1.2822 


8083 


1.2371 


8376 


1.1939 


3 


58 


7257 


1.3781 


7526 


1.3287 


7803 


1.2815 


S088 


1.2364 


8381 


1.1932 


2 


59 


7261 


1.3772 


7531 


1.3278 


7808 


1.2807 


8093 


1.2356 


8386 


1.1925 


1 


60 


7265 


1.3764 


7536 


1.3270 


7813 


1.2799 


809S 


1.2349 


8391 


1.1918 





' 


cot tan 

54° 


cot tan 
53° 


cot tan 

' 52° 


cot tan 
51° 


cot tan 
50° 




i 



NATURAL TANGENTS AND COTANGENTS. 69 



t 


40° 


41° 


42° 


43° 


44° 


t 


tan 


cot 


tan 


cot 


tan 


cot 


tan 


cot 


tan 


cot 





8391 


1.1918 


8693 


1.1504 


9004 


1.1106 


9325 


1.0724 


9657 


1.0355 


60 


1 


8396 


1.1910 


8698 


1.1497 


9009 


1.1100 


9331 


1.0717 


9663 


1.0349 


59 


2 


8401 


1.1903 


8703 


1.1490 


9015 


1.1093 


9336 


1.0711 


9668 


1.0343 


58 


3 


8406 


1.1896 


870S 


1.1483 


9020 


1.1087 


9341 


1.0705 


9674 


1.0337 


57 


4 


8411 


1.1889 


8713 


1.1477 


9025 


1.1080 


9347 


1.0699 


9679 


1.0331 


56 


5 


8416 


1.1882 


8718 


1.1470 


9030 


1.1074 


9352 


1.0692 


9685 


1.0325 


55 


6 


8421 


1.1875 


8724 


1.1463 


9036 


1.1067 


9358 


1.0686 


9691 


1.0319 


54 


7 


8426 


1.1868 


8729 


1.1456 


9041 


1.1061 


9363 


1.0680 


9696 


1.0313 


53 


8 


-8431 


1.1861 


8734 


1.1450 


9046 


1.1054 


9369 


1.0674 


9702 


1.0307 


52 


9 


8436 


1.1854 


8739 


1.1443 


9052 


1.1048 


9374 


1.0668 


9708 


1.0301 


51 


io 


8441 


1.1847 


8744 


1.1436 


9057 


1.1041 


9380 


1.0661 


9713 


1.0295 


50 


11 


8446 


1.1840 


8749 


1.1430 


9062 


1.1035 


9385 


1.0655 


9719 


1.0289 


49 


12 


8451 


1.1833 


8754 


1.1423 


9067 


1.1028 


9391 


1.0649 


9725 


1.0283 


48 


13 


8456 


1.1826 


8759 


1.1416 


9073 


1.1022 


9396 


1.0643 


9730 


1.0277 


47 


14 


8461 


1.1819 


8765 


1.1410 


9078 


1.1016 


9402 


1.0637 


9736 


1.0271 


46 


15 


8466 


1.1S12 


8770 


1.1403 


9083 


1.1009 


9407 


1.0630 


9742 


1.0265 


45 


16 


8471 


1.1806 


8775 


1.1396 


9089 


1.1003 


9413 


1.0624 


9747 


1.0259 


44 


17 


8476 


1.1799 


8780 


1.1389 


9094 


1.0996 


9418 


1.0618 


9753 


1.0253 


43 


IS 


8481 


1.1792 


8785 


1.1383 


9099 


1.0990 


9424 


1.0612 


9759 


1.0247 


42 


19 


8486 


1.1785 


8790 


1.1376 


9105 


1.0983 


9429 


1.0606 


9764 


1.0241 


41 


20 


8491 


1.1778 


8796 


1.1369 


9110 


1.0977 


9435 


1.0599 


9770 


1.0235 


40 


21 


8496 


1.1771 


8801 


1.1363 


9115 


1.0971 


9440 


1.0593 


9776 


1.0230 


39 


22 


8501 


1.1764 


8806 


1.1356 


9121 


1.0964 


9446 


1.0587 


9781 


1.0224 


38 


23 


8506 


1.1757 


8811 


1.1349 


9126 


1.0958 


9451 


1.0581 


9787 


1.0218 


37 


24 


8511 


1.1750 


8816 


1.1343 


9131 


1.0951 


9457 


1.0575 


9793 


1.0212 


36 


25 


8516 


1.1743 


8821 


1.1336 


9137 


1.0945 


9462 


1.0569 


9798 


1.0206 


35 


26 


8521 


1.1736 


8827 


1.1329 


9142 


1.0939 


9468 


1.0562 


9804 


1.0200 


34 


27 


8526 


1.1729 


8832 


1.1323 


9147 


1.0932 


9473 


1.0556 


9810 


1.0194 


33 


28 


8531 


1.1722 


8837 


1.1316 


9153 


1.0926 


9479 


1.0550 


9816 


1.0188 


31 


29 


8536 


1.1715 


8842 


1.1310 


9158 


1.0919 


9484 


1.0544 


9821 


1.0182 


31 


30 


8541 


1.1708 


8847 


1.1303 


9163 


1.0913 


9490 


1.0538 


9827 


1.0176 


30 


31 


8546 


1.1702 


8852 


1.1296 


9169 


1.0907 


9495 


1.0532 


9833 


1.0170 


29 


32 


8551 


1.1695 


8858 


1.1290 


9174 


1.0900 


9501 


1.0526 


9838 


1.0164 


28 


33 


8556 


1.1688 


8863 


1.1283 


9179 


1.0894 


9506 


1.0519 


9844 


1.0158 


27 


34 


8561 


1.1681 


8868 


1.1276 


9185 


1.0888 


9512 


1.0513 


9850 


1.0152 


26 


35 


8566 


1.1674 


8873 


1.1270 


9190 


1.0881 


9517 


1.0507 


9856 


1.0147 


25 


36 


8571 


1.1667 


887S 


1.1263 


9195 


1.0875 


9523 


1.0501 


9861 


1.0141 


24 


37 


8576 


1.1660 


8884 


1.1257 


9201 


1.0869 


9528 


1.0495 


9867 


1.0135 


23 


38 


8581 


1.1653 


8SS9 


1.1250 


9206 


1.0S62 


9534 


1.0489 


9873 


1.0129 


22 


39 


8586 


1.1647 


8894 


1.1243 


9212 


1.0856 


9540 


1.0483 


9879 


1.0123 


21 


40 


8591 


1.1640 


8899 


1.1237 


9217 


1.0850 


9545 


1.0477 


9884 


1.0117 


20 


41 


8596 


1.1633 


8904 


1.1230 


9222 


1.0843 


9551 


1.0470 


9890 


1.0111 


19 


42 


8601 


1.1626 


8910 


1.1224 


9228 


1.0837 


9556 


1.0464 


9896 


1.0105 


18 


43 


8606 


1.1619 


8915 


1.1217 


9233 


1.0831 


9562 


1.0458 


9902 


1.0099 


17 


44 


8611 


1.1612 


8920 


1.1211 


9239 


1.0824 


9567 


1.0452 


9907 


1.0094 


16 


45 


8617 


1.1606 


8925 


1.1204 


9244 


1.0818 


9573 


1.0446 


9913 


1.0088 


15 


46 


8622 


1.1599 


8931 


1.1197 


9249 


1.0812 


9578 


1.0440 


9919 


1.00S2 


14 


47 


8627 


1.1592 


8936 


1.1191 


9255 


1.0805 


95S4 


1.0434 


9925 


1.0076 


13 


48 


8632 


1.1585 


8941 


1.1184 


9260 


] .0799 


9590 


1.0428 


9930 


1.0070 


12 


49 


8637 


1.1578 


8946 


1.1178 


9266 


1.0793 


9595 


1.0422 


9936 


1.0064 


11 


50 


8642 


1.1571 


8952 


1.1171 


9271 


1.0786 


9601 


1.0416 


9942 


1.0058 


10 


51 


8647 


1.1565 


8957 


1.1165 


9276 


1.0780 


9606 


1.0410 


9948 


1.0052 


9 


52 


8652 


1.1558 


8962 


1.1158 


9282 


1.0774 


9612 


1.0404 


9954 


1.0047 


8 


53 


8657 


1.1551 


8967 


1.1152 


9287 


1.0768 


9618 


1.039S 


9959 


1.0041 


7 


54 


8662 


1.1544 


8972 


1.1145 


9293 


1.0761 


9623 


1.0392 


9965 


1.0035 


6 


55 


8667 


1.1538 


8978 


1.1139 


9298 


1.0755 


9629 


1.0385 


9971 


1.0029 


5 


56 


8672 


1.1531 


8983 


1.1132 


9303 


1.0749 


9634 


1.0379 


9977 


1.0023 


4 


57 


8678 


1.1524 


8988 


1.1126 


9309 


1.0742 


9640 


1.0373 


9983 


1.0017 


3 


58 


8683 


1.1517 


8994 


1.1119 


9314 


1.0736 


9646 


1.0367 


9988 


1.0012 


2 


59 


8688 


1.1510 


8999 


1.1113 


9320 


1.0730 


9651 


1.0361 


9994 


1.0006 


1 


60 


8693 


1.1504 


9004 


1.1106 


9325 


1.0724 


9657 


1.0355 


1.000 


1.0000 


O 




cot 


tan 


cot 


tan 


cot 


tan 


cot 


tan 


cot 


tan 




t 


49° 


48° 


47° 


46° 


45° 


/ 



70 




TABLE VII. ■ 


-TRAVEKSE 


TABLE. 






Bearing, 


Distance 1. 


Distance 2. 


Distance 3. 


Distance 4. 


Distance 5. 


Bearing. 


o t 


Lat, 


Dep, 


Lat. Dep. 


Lat. Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


o t 


15 


1.000 


0.004 


2.000 0.009 


3.000 0.013 


4.000 


0.017 


5.000 


0.022 


89 45 


30 


1.000 


0.009 


2.000 0.017 


3.000 0.026 


4.000 


0.035 


5.000 


0.044 


30 


45 


1.000 


0.013 


2.000 0.026 


3.000 0.039 


4.000 


0.052 


5.000 


0.065 


15 


1 


1.000 


0.017 


2.000 0035 


3.000 0.052 


3.999 


0.070 


4.999 


0.0S7 


89 


15 


1.000 


0.022 


2.000 0.044 


2.999 0.065 


3.999 


0.087 


4.999 


0.109 


45 


30 


1.000 


0.026 


1.999 0.052 


2.999 0.079 


3.999 


0.105 


4.998 


0.131 


30 


45 


1.000 


0.031 


1.999 0.061 


2.999 0.092 


3.998 


0.122 


4.998 


0.153 


15 


2 


0.999 


0.035 


1.999 0.070 


2.998 0.105 


3.998 


0.140 


4.997 


0.174 


88 


15 


0.999 


0.039 


1.998 0.079 


2.998 0.118 


3.997 


0.157 


4.996 


0.196 


45 


30 


0.999 


0.044 


1.998 0.087 


2.997 0.131 


3.996 


0.174 


4.995 


0.218 


30 


45 


0.999 


0.048 


1.99S 0.096 


2.997 0.144 


3.995 


0.192 


4.994 


0.240 


15 


3 


0.999 


0.052 


1.997 0.105 


2.996 0.157 


3.995 


0.209 


4.993 


0.262 


87 


15 


0.998 


0.057 


1.997 0.113 


2.995 0.170 


3.994 


0.227 


4.992 


283 


45 


30 


0.998 


0.061 


1.996 0.122 


2.994 0.183 


3.993 


0244 


4.991 


0.305 


30 


45 


0.998 


0065 


1.996 0.131 


2.994 0.196 


3.991 


0.262 


4.989 


0.327 


15 


4 


0.998 


070 


1.995 0.140 


2.993 0.209 


3.990 


0.279 


4.988 


349 


86 


15 


0.997 


0.074 


1.995 0.148 


2.992 0.222 


3.989 


0.296 


4.986 


0.371 


45 


30 


0.997 


0078 


1.994 0.157 


2.991 0.235 


3.988 


0.314 


4.985 


0.392 


30 


45 


0.997 


0.0S3 


1.993 0.166 


2.990 0.248 


3.986 


0.331 


4.983 


0.414 


15 


5 


0.996 


0.087 


1.992 0.174 


2.989 0.261 


3.985 


0.349 


4.981 


0.436 


85 


15 


0.996 


092 


1.992 0.183 


2.987 0.275 


3.983 


0.366 


4.979 


0.458 


45 


30 


0.995 


096 


1.991 0192 


2.986 0.288 


3.9S2 


0383 


4.977 


0.479 


30 


45 


0.995 


0100 


1.990 0.200 


2.985 0.301 


3.980 


0.401 


4.975 


0.501 


15 


6 


0.995 


0.105 


1.989 209 


2.984 0.314 


3.978 


0.418 


4.973 


0.523 


84 


15 


0.994 


0.109 


1.9SS 0.218 


2.982 0.327 


3.976 


0.435 


4.970 


0.544 


45 


30 


0.994 


0.113 


1.987 0.226 


2.981 0.340 


3.974 


0.453 


4.968 


0.566 


30 


45 


0.993 


0.118 


1.986 0.235 


2.979 0.353 


3.972 


0.470 


4.965 


0.5S8 


15 


7 


0.993 


0.122 


1.985 0.244 


2.978 0.366 


3.970 


0.487 


4.963 


0.609 


83 


15 


0992 


0126 


1.984 0.252 


2.976 0.379 


3.966 


0.505 


4.960 


0631 


45 


30 


0.991 


0.131 


1.983 0.261 


2.974 0.392 


3.966 


0.522 


4.957 


0.653 


30 


45 


0.991 


0.135 


1.982 0.270 


2.973 0.405 


3.963 


0.539 


4.954 


0.674 


15 


8 


0.990 


0.139 


1.981 278 


2.971 0.418 


3.961 


0.557 


4.951 


0.696 


82 


15 


0.990 


0.143 


1.979 0.287 


2.969 0.430 


3.959 


0574 


4.948 


0.717 


45 


30 


0.989 


0.148 


1.978 0.296 


2.967 0.443 


3.956 


0.591 


4.945 


0.739 


30 


45 


0.988 


0152 


1.977 0.304 


2.965 0.456 


3.953 


608 


4.942 


0.761 


15 


9 


0.988 


0.156 


1.975 0.313 


2.963 0.469 


3.951 


0.626 


4.938 


0.782 


81 


15 


0.987 


0.161 


1.974 0.321 


2.961 0.482 


3.948 


0.643 


4.935 


0.804 


45 


30 


0.9S6 


0.165 


1.973 0.330 


2.959 0.495 


3.945 


0.660 


4.931 


0.825 


30 


45 


0.986 


0.169 


1.971 0.339 


2.957 0.508 


3.942 


0.677 


4.928 


0.847 


15 


10 


0.985 


0.174 


1.970 0.347 


2.954 0.521 


3.939 


0.695 


4.924 


0.868 


80 


15 


9S4 


0.178 


1.968 0.356 


2.952 0.534 


3.936 


0.712 


4.920 


0.890 


45 


30 


0.983 


0.182 


1.967 0.364 


2.950 0.547 


3.933 


0.729 


4.916 


0.911 


30 


45 


0.982 


1S7 


1.965 0.373 


2.947 560 


3.930 


0.746 


4.912 


0.933 


15 


11 


0.982 


0.191 


1.963 0.382 


2.945 0.572 


3.927 


0.763 


4.908 


0.954 


79 


15 


0.9S1 


0.195 


1.962 0.390 


2.942 0:585 


3.923 


0.780 


4.904 


0.975 


45 


30 


980 


0.199 


1.960 '0.399 


2.940 0.598 


3.920 


0.797 


4.900 


0997 


30 


45 


0979 


0.204 


1.95S 0.407 


2.937 611 


3.916 


0.815 


4.895 


1.018 


15 


12 


0.978 


0.208 


1.956 0.416 


2.934 0624 


3.913 


0.832 


4.891 


1.040 


78 


15 


0.977 


0.212 


1.954 0.424 


2.932 0.637 


3.909 


0.S49 


4 886 


1.061 


45 


30 


0.976 


0.216 


1.953 0.433 


2.929 0.649 


3.905 


0.S66 


4.881 


1.082 


30 


45 


0.975 


0.221 


1.951 0.441 


2.926 662 


3.901 


0S83 


4.877 


1.103 


15 


13 


974 


0.225 


1.949 0.450 


2.923 0.675 


3.897 


0.900 


4.872 


1.125 


77 


15 


0.973 


0229 


1.947 0.458 


2.920 0.688 


3.894 


0.917 


4.867 


1.146 


45 


30 


0.972 


0.233 


1.945 0.467 


2.917 0.700 


3.889 


0.934 


4.862 


1.167 


30 


45 


971 


0.238 


1.943 0.475 


2.914 0.713 


3.885 


0.951 


4.857 


1.188 


15 


14 


970 


0242 


1.941 0.484 


2.911 0.726 


3.8S1 


0.968 


4.851 


1.210 


76 


15 


0.969 


0.246 


1.938 0.492 


2.90S 0.73S 


3.877 


0.985 


4.846 


1.231 


45 


30 


968 


0.250 


1.936 0.501 


2.904 0.751 


3.873 


1.002 


4.841 


1.252 


30 


45 


0.967 


0.255 


1.934 0.509 


2.901 0.764 


3.868 


1.01S 


4.835 


1.273 


15 


15 


0.966 


0.259 


1.932 0.518 


2.89S 0.776 


3.864 


1.035 


4.830 


1.294 


75 


o r 


Dep. 


Lat. 


Dep. Lat. 


Dep, Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


o t 


Bearing 


Distance 1. 


Distance 2. 


Distance 3. 


Distance 4. 


Distance 5. 


Bearing. 



75°-90 c 













o°- 


-15° 










71 


Bearing. 


Distance 6. 


Distance 7. 


Distance 8. 


Distance 9. 


Distance 10. 


Bearing, 


o r 


Lat. 


Dep, 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


o r 


15 


6.000 


026 


7.000 


0.031 


8.000 


0.035 


9 000 


0.039 


10.000 


0.044 


89 45 


30 


6000 


0.052 


7.000 


0.061 


8.000 


0.070 


9000 


0.079 


10.000 


0.087 


30 


45 


5.999 


0.079 


6.999 


0.092 


7.999 


0.105 


S.999 


0.118 


9.999 


0.131 


15 


1 


5.999 


0.105 


6.999 


0.122 


7.999 


0.140 


8.999 


0.157 


9.999 


0.175 


89 


15 


5.999 


0.131 


6.99S 


0.153 


7.99S 


0.175 


8.998 


0.196 


9.998 


0.218 


45 


30 


5.998 


0.157 


6.99S 


0.183 


7.997 


0.209 


8 997 


0.236 


9.997 


0.262 


30 


45 


5.997 


0.1S3 


6.997 


0.214 


7.996 


0.244 


8.996 


0.275 


9.995 


0.305 


15 


2 


5.996 


0.209 


6.996 


0.244 


7.995 


0.279 


8.995 


0.314 


9.994 


0.349 


88 


15 


5.995 


0.236 


6.995 


0.275 


7.994 


0.314 


8.993 


0.353 


9.992 


0.393 


45 


30 


5.994 


0.262 


6.993 


0.305 


7.992 


0.349 


8.991 


0.393 


9.991 


0.436 


30 


45 


5.993 


0.2S8 


6.992 


0.336 


7.991 


0.384 


8.990 


0.432 


9.989 


0.4S0 


15 


3 


5.992 


0314 


6.990 


0.366 


7.989 


0.419 


8.988 


0.471 


9.986 


0.523 


87 


15 


5.990 


0.340 


6.989 


0.397 


7.9S7 


0.454 


8.986 


0.510 


9.984 


0.567 


45 


30 


5.9S9 


0.366 


6.9S7 


0.427 


7.985 


0.48S 


8.983 


0.549 


9.981 


0.611 


30 


45 


5.9S7 


0.392 


6.985 


0.458 


7.983 


0.523 


8.981 


0.589 


9.979 


0.654 


15 


4 


5.9S5 


0.419 


6.983 


0.4SS 


7.981 


0.558 


8.978 


0.628 


9.976 


698 


86 


15 


5.9S4 


0.445 


6.9S1 


0.519 


7.978 


0.593 


8.975 


0.667 


9.973 


0.741 


45 


30 


5.9S2 


0.471 


6.97S 


0.549 


7.975 


0.628 


8.972 


0.706- 


9.969 


0.785 


30 


45 


5.979 


0.497 


6.976 


0.580 


7.973 


0.662 


8.969 


0.745 


9.966 


0.828 


15 


5 


5.977 


'0.523 


6.973 


0.610 


7.970 


0.697 


8.966 


0.784 


9.962 


0.872 


85 


15 


5.975 


0549 


6.971 


0.641 


7.966 


0.732 


8.962 


0.824 


9.958 


0.915 


45 


30 


5.972 


575 


6.968 


0.671 


7.963 


0.767 


8.959 


0.863 


9.954 


0.959 


30 


45 


5.970 


601 


6.965 


0.701 


7.960 


0.802 


8.955 


0.902 


9.950 


1.002 


15 


6 


5.967 


0.627 


6.962 


0.732 


7.956 


0.836 


8.951 


0.941 


9.945 


1.045 


84 


15 


5.964 


0.653 


6.958 


0.762 


7.952 


0.871 


S.947 


0.980 


9.941 


1.089 


45 


30 


5.961 


0.679 


6.955 


0.792 


7.949 


0.906 


8.942 


1.019 


9.936 


1.132 


30 


45 


5.95S 


0.705 


6.951 


0.823 


7.945 


0.940 


8938 


1.058 


9.931 


1.175 


15 


7 


5.955 


0.731 


6.948 


0.853 


7.940 


0.975 


8.933 


1.097 


9.926 


1.219 


83 


15 


5.952 


0.757 


6.944 


0.883 


7.936 


1.010 


8.928 


1.136 


9.920 


1.262 


45 


30 


5.949 


0.7S3 


6.940 


0.914 


7.932 


1.044 


8.923 


1.175 


9.914 


1.305 


30 


45 


5.945 


0.809 


6.936 


0.944 


7.927 


1.079 


8.918 


1.214 


9.909 


1.349 


15 


8 


5.942 


0.835 


6.932 


0.974 


7.922 


1.113 


8.912 


1.253 


9.903 


1.392 


82 


15 


5.93S 


0.861 


6.928 


1.004 


7.917 


1.148 


8.907 


1.291 


9.897 


1.435 


45 


30 


5.934 


0.8S7 


6 923 


1.035 


7.912 


1.182 


8.901 


1.330 


9.890 


1.478 


30 


45 


5.930 


913 


6.919 


1.065 


7.907 


1.217 


8.895 


1.369 


9.884 


1.521 


15 


9 


5.926 


0.939 


6.914 


1.095 


7.902 


1.251 


8.889 


1.408 


9.877 


1.564 


81 


15 


5.922 


0.964 


6.909 


1.125 


7.896 


1.286 


8.883 


1.447 


9.870 


1.607 


45 


30 


5.918 


0.990 


6.904 


1.155 


7.890 


1.320 


8.877 


1.485 


9.863 


1.651 


30 


45 


5.913 


1.016 


6.899 


1.185 


7.884 


1.355 


8.870 


1.524 


9.856 


1.694 


.15 


10 


5.909 


1.042 


6.894 


1.216 


7.878 


1.389 


8.863 


1.563 


9.848 


1.737 


80 


15 


5.904 


1.068 


6.88S 


1.246 


7.872 


1.424 


8.856 


1.601 


9.840 


1.779 


45 


30 


5.900 


1.093 


6.S83 


1.276 


7.866 


1.458 


8.849 


1.640 


9.833 


1.822 


30 


45 


5.895 


1.119 


6.877 


1.306 


7.860 


1.492 


8.842 


1.679 


9.825 


1.865 


15 


11 


5.S90 


1.145 


6.871 


1.336 


7.853 


1.526 


8.835 


1.717 


9.816 


1.908 


79 


15 


5.885 


1.171 


6.866 


1.366 


7.846 


1.561 


8.827 


1.756 


9.808 


1.951 


45 


30 


5. 880 


1.196 


6.859 


1.396 


7.839 


1.595 


8.819 


1.794 


9.799 


1.994 


30 


45 


5.874 


1.222 


6.853 


1425 


7.832 


1.629 


8.811 


1.833 


9.791 


2036 


15 


12 


5.869 


1.247 


6.S47 


1.455 


7.825 


1663 


8.803 


1.871 


9 782 


2.079 


78 


15 


5.S63 


1.273 


6.841 


1.485 


7.81S 


1.697 


8.795 


1.910 


9.772 


2.122 


45 


30 


5.858 


1.299 


6.834 


1.515 


7.S10 


1.732 


8.787 


1.948 


9.763 


2.164 


30 


45 


5.852 


1.324 


6.827 


1.545 


7.803 


1.766 


8.778 


1.986 


9.753 


2.207 


15 


13 


5.846 


1.350 


6.821 


1.575 


7.795 


1.800 


8.769 


2.025 


9.744 


2.250 


77 


15 


5.840 


1.375 


6.814 


1.604 


7.7S7 


1.834 


8.760 


2.063 


9.734 


2.292 


45 


30 


5.834 


1.401 


6.807 


1.634 


7.779 


1.868 


8.751 


2.101 


9.724 


2.335 


30 


45 


5.828 


1.426 


6.799 


1.664 


7.771 


1.902 


8.742 


2139 


9.713 


2.377 


15 


14 


5.822 


1.452 


6.792 


1.693 


7.762 


1.935 


8.733 


2.177 


9.703 


2.419 


76 


15 


5.S15 


1.477 


6.785 


1.723 


7.754 


1.969 


8.723 


2.215 


9.692 


2.462 


45 


30 


5.S09 


1.502 


6777 


1.753 


7.745 


2.003 


8.713 


2.253 


9.6S2 


2.504 


30 


45 


5.802 


1.52S 


6.769 


1.7S2 


7.736 


2.037 


8.703 


2.291 


9.671 


2.546 


15 


15 


5.796 


1.553 


6.761 


1.812 


7.727 


2.071 


S.693 


2.329 


9.659 


2.588 


75 


o f 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


o t 


Bearing. 


Distance 6. 


Distance 7. 


Distance 8. 


Distance 9. 


Distance 10. 


Bearing. 



75°-90 c 



72 










15°- 


-30° 










Bearing. 


Distance 1. 


Distance 2. 


Distance 3. 


Distance 4. 


Distance 5. 


Bearing. 


o t 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


O f 


15 15 


0.965 


0263 


1.930 


0.526 


2.894 


0.789 


3.859 


1.052 


4.824 


1.315 


74 45 


30 


0.964 


0.267 


1.927 


0.534 


2.891 


0.802 


3.855 


1.069 


4.818 


1.336 


30 


45 


0.962 


0.271 


1.925 


0.543 


2.887 


0.814 


3.850 


1.086 


4.812 


1.357 


15 


16' 


0.961 


0.276 


1.923 


0.551 


2.8S4 


0.827 


3.845 


1.103 


4.806 


1.378 


74 


15 


0.960 


0.280 


1.920 


0.560 


2.880 


0.839 


3.840 


1.119 


4.800 


1.399 


45 


30 


0.959 


0.284 


1.918 


0.568 


2.876 


0.852 


3.835 


1.136 


4.794 


1.420 


30 


45 


0.958 


0.288 


1.915 


0.576 


2.873 


0.865 


3.830 


1.153 


4.788 


1.441 


15 


17 


0956 


0.292 


1.913 


0.585 


2.S69 


0.877 


3.S25 


1.169 


4.782 


1.462 


73 


15 


0.955 


0.297 


1.910 


0.593 


2.865 


0.890 


3.820 


1.186 


4.775 


1.483 


45 


30 


0.954 


0.301 


1.907 


0.601 


2.861 


0.902 


3.815 


1.203 


4.769 


1.504 


30 


45 


0.952 


0.305 


1.905 


0.610 


2.857 


0.915 


3.810 


1.220 


4.762 


1.524 


15 


18 


0.951 


0.309 


1.902 


0.618 


2.853 


0.927 


3.804 


1.236 


4.755 


1.545 


72 


15 


0.950 


0.313 


1.899 


0.626 


2.849 


0.939 


3.799 


1.253 


4.748 


1.566 


45 


30 


0.948 


0.317 


1.897 


0.635 


2.845 


0.952 


3.793 


1.269 


4.742 


1.587 


30 


45 


0.947 


0.321 


1.894 


0.643 


2.841 


0.964 


3 788 


1.286 


4.735 


1.607 


15 


19 


0.946 


0.326 


1.891 


0.651 


2.837 


0.977 


3.782 


1.302 


4.728 


1.62S 


71 


15 


0.944 


0.330 


1.S8S 


0.659 


2.S32 


0.989 


3.776 


1.319 


4.720 


1.648 


45 


30 


0.943 


0.334 


1.885 


0.668 


2.828 


1.001 


3.771 


1.335 


4.713 


1.669 


30 


45 


0.941 


0.338 


1.882 


0.676 


2.824 


1.014 


3.765 


1.352 


4.706 


1.690 


15 


20 


0.940 


0.342 


1.879 


0.684 


2.819 


1.026 


3.759 


1.368 


4.698 


1.710 


70 


15 


0.938 


0.346 


1.876 


692 


2.815 


1.038 


3.753 


1.384 


4.691 


1.731 


45 


30 


0.937 


0350 


1.873 


0.700 


2.810 


1.051 


3.747 


1.401 


4.683 


1.751 


30 


45 


0.935 


0.354 


1.870 


0709 


2.805 


1.063 


3.741 


1.417 


4.676 


1.771 


15 


21 


0.934 


0.358 


1.867 


0.717 


2.801 


1.075 


3.734 


1.433 


4.668 


1.792 


69 


15 


0.932 


0.362 


1.864 


0.725 


2.796 


1.087 


3.728 


1.450 


4.660 


1.812 


45 


30 


0.930 


0.367 


1.861 


0.733 


2.791 


1.100 


3.722 


1.466 


4.652 


1.833 


30 


45 


0.929 


0.371 


1.858 


0.741 


2.786 


1.112 


3.715 


1.482 


4.644 


1.853 


15 


22 


0.927 


0.375 


1.854 


0.749 


2.782 


1.124 


3.709 


1.498 


4.636 


1.873 


68 


15 


0.926 


379 


1.851 


0.757 


2.777 


1.136 


3.702__ 


1.515 


4.628 


1.893 


45 


30 


0.924 


0.383 


1.848 


0.765 


2.772 


1.148 


3.696,1.531 


4.619 


1.913 


30 


45 


0.922 


0.387 


1.844 


0.773 


2.767 


1.160 


3.689 


1.547 


' 4.611 


1.934 


15 


23 


0.921 


0.391 


1.841 


0.781 


2.762 


1.172 


3.682 


1.563 


4.603 


1.954 


67 


15 


0.919 


0.395 


1.S3S 


0.789 


2.756 


1.184 


3.675 


1.579 


4.594 


1.974 


45 


30 


0.917 


0.399 


1.834 


0.797 


2.751 


1.196 


3.668 


1.595 


4.585 


1.994 


30 


45 


0.915 


403 


1.831 


0.805 


2.746 


1.208 


3.661 


1.611 


4.577 


2.014 


15 


24 


0.914 


0.407 


1.827 


0.813 


2.741 


1.220 


3.654 


1.627 


4.568 


2.034 


66 


15 


0.912 


0.411 


1.824 


0.821 


2.735 


1.232 


3.647 


1.643 


4.559 


2.054 


45 


30 


0.910 


0.415 


1.820 


0.S29 


2.730 


1.244 


3.640 


1.659 


4.550 


2.073 


30 


45 


0.90S 


0.419 


1.816 


0.837 


2.724 


1.256 


3.633 


1.675 


4.541 


2.093 


15 


25 


0.906 


0.423 


1.813 


0.845 


2.719 


1.26S 


3.625 


1.690 


4.532 


2.113 


65 


15 


0.904 


0.427 


1.809 


0.853 


2.713 


1.28*0 


3.618 


1.706 


4.522 


2.133 


45 


30 


0.903 


0.431 


1.805 


0.861 


2.708 


1.292 


3.610 


1.722 


4.513 


2.153 


30 


45 


0.901 


0.434 


1.801 


0.869 


2.702 


1.303 


3.603 


1.73S 


4.503 


2.172 


15 


26 


0.S99 


0.438 


1.798 


0.877 


2.696 


1.315 


3.595 


1.753 


4.494 


2.192 


64 


15 


0S97 


0.442 


1.794 


0.885 


2.691 


1.327 


3.587 


1.769 


4.484 


2.211 


45 


30 


0.895 


0.446 


1.790 


892 


2.685 


1.339 


3.580 


1.785 


4.475 


2.231 


30 


45 


0.S93 


0.450 


1.786 


0.900 


2.679 


1.350 


3.572 


1.800 


4.465 


2.250 


15 


27 


0.891 


0.454 


1.782 


0.908 


2.-673 


1.362 


3.564 


1.816 


4.455 


2.270 


63 


15 


0.889 


0.458 


1.77S 


0.916 


2.667 


1.374 


3.556 


1.831 


4.445 


2.289 


45 


30 


0.8S7 


0.462 


1.774 


0.923 


2.661 


1.385 


3.548 


1.847 


4.435 


2.309 


30 


45 


0885 


0.466 


1.770 


0.931 


2.655 


1.397 


3.540 


1.862 


4.425 


2.328 


15 


28 


0.S83 


0.469 


1.766 


0.939 


2 649 


1.40S 


3.532 


1.878 


4.415 


2.347 


62 


15 


0.881 


0.473 


1.762 


0.947 


2.643 


1.420 


3.524 


1.893 


4.404 


2.367 


45 


30 


879 


0.477 


1.758 


0.954 


2.636 


1.431 


3.515 


1.909 


4.394 


2.386 


30 


45 


0.877 


0.481 


1.753 


0.962 


2.630 


1.443 


3.507 


1.924 


4.3S4 


2.405 


15 


29 


0.875 


0.485 


1.749 


0.970 


2.624 


1.454 


3.498 


1.939 


4.373 


2.424 


61 


15 


0.872 


0.489 


1.745 


0.977 


2.617 


1.466 


3.490 


1.954 


4.362 


2.443 


45 


30 


0.870 


0.492 


1.741 


0.985 


2.611 


1.477 


3.481 


1.970 


4.352 


2.462 


30 


45 


0.868 


0.496 


1.736 


0.992 


2.605 


1.489 


3.473 


1.985 


4.341 


2.481 


15 


30 


0.866 


0.500 


1.732 


1.000 


2.598 


1.500 


3.464 


2.000 


4.330 


2.500 


60 


O f 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


o r 


Bearing. 


Distance 1. 


Distance 2. 


Distance 3. 


Distance 4. 


Distance 5. 


Bearing. 



60 o -75 ( 













15°- 


-30 


o 








73 


Bearing. 


Distance 6. 


Distance 7. 


Distance 8. 


Distance 9. 


Distance 10. 


Bearing. 


o t 


Lat. 


Dep, 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


o r 


15 15 


5.7S9 


1.578 


6.754 


1.S41 


7.71S 


2.104 


8.683 


2.367 


9.64S 


2.630 


74 45 


30 


5.782 


1.603 


6.745 


1.871 


7.709 


2.138 


8.673 


2.405 


9.636 


2.672 


30 


45 


5.775 


1.629 


6.737 


1.900 


7.700 


2.172 


8.662 


2.443 


9.625 


2.714 


15 


16 


5.76S 


1.654 


6.729 


1.929 


7.690 


2.205 


8.651 


2.481 


9.613 


2.756 


74 


15 


5.760 


1.679 


6.720 


1.959 


7.6S0 


2.239 


8.640 


2.518 


9.601 


2.798 


45 


30 


5.753 


1.704 


6.712 


1.988 


7.671 


2.272 


S.629 


2.556 


9.5SS 


2.840 


30 


45 


5.745 


1.729 


6.703 


2.017 


7.661 


2.306 


8.618 


2.594 


9.576 


2.882 


15 


17 


5.73S 


1.754 


6.694 


2.047 


7.650 


2.339 


S.607 


2.631 


9.563 


2.924 


73 


15 


5.730 


1.779 


6.685 


2.076 


7.640 


2.372 


8.595 


2.669 


9.550 


2.965 


45 


30 


5.722 


1.S04 


6.676 


2.105 


7.630 


2.406 


8.583 


2.706 


9.537 


3 007 


30 


45 


5.714 


1.829 


6.667 


2.134 


7.619 


2.439 


8.572 


2.744 


9.524 


3.049 


15 


18 


5.706 


1.854 


6.657 


2.163 


7.608 


2.472 


8.560 


2.781 


9.511 


3.090 


72 


15 


5.698 


1.S79 


6.648 


2.192 


7.598 


2.505 


8.547 


2.818 


9.497 


3.132 


45 


30 


5.690 


1.904 


6.63S 


2.221 


7.5S7 


2.538 


8.535 


2.856 


9.483 


3.173 


30 


45 


5.6S2 


1.929 


6.629 


2.250 


7.575 


2.572 


8.522 


2.893 


9.469 


3.214 


15 


19 


5.673 


1.953 


6.619 


2.279 


7.564 


2.605 


8.510 


2.930 


9.455 


3.256 


71 


15 


5.665 


1.978 


6.609 


2.30S 


7.553 


2.63S 


8.497 


2.967 


9.441 


3.297 


45 


30 


5.656 


2.003 


6.598 


2.337 


7.541 


2.670 


8.484 


3.004 


9.426 


3.338 


30 


45 


5.647 


2.02S 


6.588 


2.365 


7.529 


2.703 


8.471 


3.041 


9.412 


3.379 


15 


20 


5.638 


2.052 


6.57S 


2.394 


7.518 


2.736 


8.457 


3.078 


9.397 


3.420 


70 


15 


5.629 


2.077 


6.567 


2.423 


7.506 


2.769 


8.444 


3.115 


9.382 


3.461 


45 


30 


5.620 


2.101 


6.557 


2.451 


7.493 


2.802 


8.430 


3.152 


9.367 


3.502 


30 


45 


5.611 


2.126 


6.546 


2.480 


7.481 


2.834 


8.416 


3.189 


9.351 


3.543 


15 


21 


5.601 


2.150 


6.535 


2.509 


7.469 


2.867 


8.402 


3.225 


9.336 


3.584 


69 


15 


5.592 


2.175 


6.524 


2.537 


7.456 


2.900 


8.388 


3.262 


9.320 


3.624 


45 


30 


5.582 


2.199 


6.513 


2.566 


7.443 


2.932 


8.374 


3.299 


9.304 


3.665 


30 


45 


5.573 


2.223 


6.502 


2.594 


7.430 


2.964 


8.359 


3.335 


9.2S8 


3.706 


15 


22 


5.563 


2.248 


6.490 


2.622 


7.417 


2.997 


8.345 


3.371 


9.272 


3.746 


68 


" 15 


5.553 


2.272 


6.479 


2.651 


7.404 


3.029 


8.330 


3.408 


9.255 


3.787 


45 


30 


5.543 


2.296 


6.467 


2.679 


7.391 


3.061 


S.315 


3.444 


9.239 


3.827 


30 


45 


5.533 


2.320 


6.455 


2.707 


7.378 


3.094 


8.300 


3.480 


9.222 


3.867 


15 


23 


5.523 


2.344 


6.444 


2.735 


7.364 


3.126 


8.285 


3.517 


9.205 


3.907 


67 


15 


5.513 


2.368 


6.432 


2.763 


7.350 


3.158 


8.269 


3.553 


9.188 


3.947 


45 


30 


5.502 


2.392 


6.419 


2.791 


7.336 


3.190 


8.254 


3.589 


9.171 


3.988 


30 


45 


5.492 


2.416 


6.407 


2.819 


7.322 


3.222 


8.238 


3.625 


9.153 


4.02S 


15 


24 0, 


5.481 


2.440 


6.395 


2.847 


7.308 


3.254 


8.222 


3.661 


9.136 


4.067 


66 


15 


5.471 


2.464 


6.382 


2.875 


7.294 


3.286 


8.206 


3.696 


9.118 


4.107 


45 


30 


5.460 


2.488 


6.370 


2.903 


7.280 


3.318 


8.190 


3.732 


9.100 


4.147 


30 


45 


5.449 


2.512 


6.357 


2.931 


7.265 


3.349 


8.173 


3.768 


9.0S1 


4.187 


15 


25 


5.43S 


2.536 


6.344 


2.95S 


7.250 


3.381 


8.157 


3.804 


9.063 


4.226 


65 


15 


5.427 


2.559 


6.331 


2.9S6 


7.236 


3.413 


8140 


3.839 


9.045 


4.266 


45 


30 


5.416 


2.5S3 


6.318 


3.014 


7.221 


3.444 


8.123 


3.875 


9.026 


4.305 


30 


45 


5.404 


2.607 


6.305 


3.041 


7.206 


3.476 


8.106 


3.910 


9.007 


4.345 


15 


26 


5.393 


2.630 


6.292 


3.069 


7.190 


3507 


8089 


3.945 


S.9SS 


4.3S4 


64 


15 


5.3S1 


2.654 


6.278 


3.096 


7.175 


3.538 


8.072 


3.9S1 


8.969 


4.423 


45 


30 


5.370 


2.677 


6.265 


3123 


7.160 


3.570 


8.054 


4.016 


8.949 


4.462 


30 


45 


5.358 


2.701 


6.251 


3.151 


7.144 


3.601 


8.037 


4.051 


8.930 


4.501 


15 


27 


5.346 


2.724 


6.237 


3.178 


7.128 


3.632 


8.019 


4.0S6 


8 910 


4.540 


63 


15 


5.334 


2.747 


6.223 


3.205 


7.112 


3.663 


8.001 


4.121 


8.890 


4.579 


45 


30 


5.322 


2.770 


6.209 


3.232 


7.096 


3.694 


7.983 


4.156 


8.870 


4.618 


30 


45 


5.310 


2.794 


6.195 


3.259 


7.080 


3.725 


7.965 


4.190 


8.850 


4.656 


15 


28 


5.298 


2.817 


6.181 


3.286 


7.064 


3.756 


7.947 


4.225 


8.829 


4.695 


62 


15 


5.285 


2.840 


6.166 


3.313 


7.047 


3.787 


7.928 


4.260 


S.809 


4.733 


45 


30 


5.273 


2.863 


6.152 


3.340 


7.031 


3.817 


7.909 


4.294 


8.788 


4.772 


30 


45 


5.260 


2.886 


6.137 


3.367 


7.014 


3.848 


7.S91 


4329 


8.767 


4.810 


15 


29 


5.248 


2.909 


6.122 


3.394 


6.997 


3.878 


7.872 


4.363 


8.746 


4.848 


61 


15 


5.235 


2.932 


6.107 


3.420 


6.9S0 


3.909 


7.852 


4.398 


8.725 


4.8S6 


45 


30 


5.222 


2.955 


6 093 


3.447 


6.963 


3.939 


7.833 


4.432 


8.704 


4.924 


30 


45 


5.209 


2.977 


6.077 


3.474 


6.946 


3.970 


7.814 


4.466 


8.682 


4.962 


15 


30 


5.196 


3.000 


6.062 


3.500 


6.928 


4.000 


7.794 


4.500 


8.660 


5.000 


60 


O f 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


t 


Bearing. 


Distance 6. 


Distance 7. 


Distance 8. 


Distance 9. 


Distance 10. 


Bearing. 



60°-75 c 



74 










30°- 


-45 


O 










Bearing. 


Distance 1. 


Distance 2. 


Distance 3. 


Distance 4. 


Distance 5. 


Bearing. 


o r 


Lat< 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


o t 


30 15 


0.864 


0.504 


1.728 


LOOS 


2.592 


1.511 


3.455 


2.015 


4.319 


2.519 


59 45 


30 


0.862 


0.508 


1.723 


1.015 


2.585 


1.523 


3.447 


2.030 


4.308 


2.538 


30 


45 


0.859 


0.511 


1.719 


1.023 


2.578 


1.534 


3.438 


2.045 


4.297 


2.556 


15 


31 


0.857 


0.515 


1.714 


1.030 


2.572 


1.545 


3.429 


2.060 


4.286 


2.575 


59 


15 


0.855 


0.519 


1.710 


1.038 


2.565 


1.556 


3.420 


2.075 


4.275 


2.594 


45 


30 


0.853 


0.522 


1.705 


1.045 


2.558 


1.567 


3.411 


2.090 


4.263 


2.612 


30 


45 


0.850 


0526 


1.701 


1.052 


2.551 


1.579 


3.401 


2.105 


4.252 


2.631 


15 


32 


0.848 


0.530 


1.696 


1.060 


2.544 


1.590 


3.392 


2.120 


4.240 


2 650 


58 


15 


0.846 


0.534 


1.691 


1.067 


2.537 


1.601 


3.383 


2.134 


4.229 


2.668 


45 


30 


0.843 


0.537 


1.687 


1.075 


2.530 


1.612 


3.374 


2.149 


4.217 


2.686 


30 


45 


0.841 


0.541 


1.682 


1.082 


2.523 


1.623 


3.364 


2.164 


4.205 


2.705 


15 


33 


0.839 


0.545 


1.677 


1.089 


2.516 


1.634 


3.355 


2.179 


4.193 


2.723 


57 


15 


0.836 


0.54S 


1.673 


1.097 


2.509 


1.645 


3.345 


2.193 


4.181 


2741 


45 


30 


0.834 


0.552 


1.668 


1.104 


2.502 


1.656 


3.336 


2.208 


4.169 


2.760 


30 


45 


0.831 


0.556 


1.663 


1.111 


2.494 


1.667 


3.326 


2.222 


4.157 


2.778 


15 


34 


0.829 


0.559 


1.658 


1.118 


2.487 


1.678 


3.316 


2.237 


4.145 


2.796 


56 


15 


0.827 


0.563 


1.653 


1.126 


2.480 


1.688 


3.306 


2.251 


4.133 


2.814 


45 


30 


0.824 


0.566 


1.648 


1.133 


2.472 


1.699 


3.297 


2.266 


4.121 


2.832 


30 


45 


0.822 


0.570 


1.643 


1.140 


2.465 


1.710 


3.287 


2.280 


4.108 


2.850 


15 


35 


0.819 


0.574 


1.638 


1.147 


2.457 


1.721 


3.277 


2.294 


4.096 


2.868 


55 


15 


0.817 


0.577 


1.633 


1.154 


2.450 


1.731 


3.267 


2.309 


4.083 


2.886 


45 


30 


0.814 


0.581 


1.628 


1.161 


2.442 


1.742 


3.257 


2.323 


4.071 


2.904 


30 


45 


0.812 


584 


1.623 


1.168 


2.435 


1.753 


3.246 


2.337 


4.058 


2.921 


15 


36 


0.809 


0.588 


1.618 


1.176 


2.427 


1.763 


3.236 


2.351 


4.045 


2.939 


54 


15 


0.S06 


0.591 


1.613 


1.183 


2.419 


1.774 


3.226 


2.365 


4.032 


2.957 


45 


30 


0.804 


0.595 


1.608 


1.190 


2.412 


1.784 


3.215 


2.379 


4.019 


2.974 


30 


45 


0.801 


0.598 


1.603 


1.197 


2.404 


1.795 


3.205 


2.393 


4.006 


2.992 


15 


37 


0.799 


0.602 


1.597 


1.204 


2.396 


1.805 


3.195 


2.407 


3.993 


3.009 


53 


15 


0.796 


0.605 


1.592 


1.211 


2.388 


1.816 


3.184 


2.421 


3.980 


3.026 


45 


30 


0.793 


0.609 


1.587 


1.218 


2.380 


1.826 


3.173* 2.435 


3.967 


3.044 


30 


45 


0.791 


0.612 


1.581 


1.224 


2.372 


1.837 


3.163' 


2.449 • 


3.953 


3.061 


15 


38 


0.788 


0.616 


1.576 


1.231 


2.364 


1.847 


3.152 


2.463 


3 940 


3.078 


52 


15 


0.785 


0.619 


1.571 


1.238 


2.356 


1.857 


3.141 


2.476 


3.927 


3.095 


45 


30 


0.783 


0.623 


1.565 


1.245 


2.348. 


1.868 


3.130 


2.490 


3.913 


3.113 


30 


45 


0.780 


0.626 


1.560 


1.252 


2.340 


1.878 


3.120 


2.504 


3.899 


3.130 


15 


39 


0.777 


0.629 


1.554 


1.259 


2.331 


1.888 


3.109 


2.517 


3.886 


3.147 


51 


15 


0.774 


0.633 


1.549 


1.265 


2.323 


1.898 


3.098 


2.531 


3.872 


3.164 


45 


30 


0.772 


0.636 


1.543 


1.272 


2.315 


1.908 


3.086 


2.544 


3.858 


3.180 


30 


45 


0.769 


0.639 


1.538 


1.279 


2.307 


1.918 


3.075 


2.558 


3.844 


3.197 


15 


40 


0.766 


0.643 


1.532 


1.286 


2.298 


1.928 


3 064 


2.571 


3.830 


3.214 


50 


15 


0.763 


0.646 


1.526 


1.292 


2.290 


1.938 


3 053 


2.584 


3.816 


3.231 


45 


30 


0.760 


0.649 


1.521 


1.299 


2.281 


1.948 


3.042 


2.598 


3.802 


3.247 


30 


45 


0.758 


0653 


1.515 


1.306 


2.273 


1.958 


3.030 


2.611 


3.788 


3.264 


15 


41 


0.755 


656 


1.509 


1.312 


2.264 


1.968 


3.019 


2.624 


3.774 


3.280 


49 


15 


0.752 


0.659 


1.504 


1.319 


2.256 


1.978 


3.007 


2.637 


3759 


3.297 


45 


30 


0.749 


0.663 


1.498 


1325 


2.247 


1.988 


2.996 


2.650 


3.745 


3.313 


30 


45 


0.746 


0.666 


1.492 


1.332 


2.238 


1.998 


2.984 


2.664 


3.730 


3.329 


15 


42 


0.743 


0.669 


1,486 


1.338 


2.229 


2.007 


2.973 


2.677 


3.716 


3.346 


48 


15 


0.740 


0.672 


1.480 


1.345 


2.221 


2.017 


2.961 


2.689 


3.701 


3.362 


45 


30 


0.737 


0.676 


1.475 


1.351 


2.212 


2 027 


2.949 


2.702 


3.686 


3.378 


30 


45 


0.734 


0.679 


1.469 


1.358 


2.203 


2.036 


2.937 


2.715 


3.672 


3.394 


15 


43 


0.731 


682 


1.463 


1.364 


2.194 


2.046 


2.925 


2.728 


3.657 


3.410 


47 


15 


0.728 


0.685 


1.457 


1.370 


2.185 


2.056 


2.913 


2.741 


3.642 


3.426 


45 


30 


0.725 


0.688 


1.451 


1.377 


2.176 


2.065 


2.901 


2.753 


3.627 


3.442 


30 


45 


0.722 


0.692 


1.445 


1.383 


2.167 


2.075 


2.889 


2 766 


3.612 


3.458 


15 


44 


0.719 


0.695 


1.439 


1.389 


2.158 


2.084 


2.877 


2.779 


3.597 


3.473 


46 


15 


0.716 


0.698 


1.433 


1.396 


2.149 


2.093 


2.865 


2.791 


3.582 


3.489 


45 


30 


0.713 


0.701 


1.427 


1.402 


2.140 


2.103 


2.853 


2.804 


3.566 


3.505 


30 


45 


0.710 


0.704 


1.420 


1.408 


2.131 


2.112 


2S41 


2.816 


3.551 


3.520 


15 


45 


0.707 


0.707 


1.414 


1.414 


2.121 


2.121 


2.828 


2.828 


3.536 


3.536 


45 


o r 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


O f 


Bearing, 


Distance 1. 


Distance 2. 


Distance 3. 


Distance 4. 


Distance 5. 


Bearing. 



45° -60°" 













30°- 


-45 


O 








75 


Bearing. 


Distance 6. 


Distance 7. 


Distance 8. 


Distance 9. 


Distance 10. 


Bearing. 


O f 


Lat, 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


o t 


30 15 


5.183 


3.023 


6.047 


3.526 


6.911 


4.030 


7.775 


4.534 


8.638 


5.038 


59 45 


30 


5.170 


3.045 


6.031 


3.553 


6.893 


4.060 


7.755 


4.568 


8.616 


5.075 


30 


45 


5.156 


3.068 


6.016 


3.579 


6.875 


4.090 


7.735 


4.602 


8.594 


5.113 


15 


31 


5.143 


3.090 


6.000 


3.605 


6.857 


4.120 


7.715 


4.635 


8.572 


5.150 


59 


15 


5.129 


3.113 


5.984 


3.631 


6.839 


4.150 


7.694 


4.669 


8.549 


5.188 


45 


30 


5.116 


3.135 


5.968 


3.657 


6.821 


4.180 


7.674 


4.702 


8.526 


5.225 


30 


45 


5.102 


3.157 


5.952 


3.683 


6.803 


4.210 


7.653 


4.736 


8.504 


5.262 


15 


32 


5.088 


3.180 


5.936 


3.709 


6.784 


4.239 


7.632 


4.769 


8.481 


5.299 


58 


15 


.5.074 


3.202 


5.920 


3.735 


6.766 


4.269 


7.612 


4.802 


8.457 


5.336 


45 


30 


5.060 


3.224 


5.904 


3.761 


6.747 


4.298 


7.591 


4.836 


8.434 


5.373 


30 


45 


5.046 


3.246 


5.887 


3.787 


6.728 


4.328 


7.569 


4.869 


8.410 


5.410 


15 


33 


5.032 


3.268 


5.871 


3.812 


6.709 


4.357 


7.548 


4.902 


8.387 


5.446 


57 


15 


5.018 


3.290 


5.854 


3.838 


6.690 


4.386 


7.527 


4.935 


8.363 


5.483 


45 


30 


5.003 


3.312 


5.837 


3.864 


6.671 


4.416 


7.505 


4.967 


8.339 


5.519 


30 


45 


4.989 


3.333 


5.820 


3.889 


6.652 


4.445 


7.483 


5.000 


8.315 


5.556 


15 


34 


4.974 


3.355 


5.803 


3.914 


6.632 


4.474 


7.461 


5.033 


8.290 


5.592 


56 


15 


4.960 


3.377 


5.786 


3.940 


6.613 


4.502 


7.439 


5.065 


8.266 


5.628 


45 


30 


4.945 


3.398 


5.769 


3.965 


6.593 


4.531 


7.417 


5.098 


8.241 


5.664 


30 


45 


4.930 


3.420 


5.752 


3.990 


6.573 


4.560 


7.395 


5.130 


8.217 


5.700 


15 


35 


4.915 


3.441 


5.734 


4.015 


6.553 


4.5S9 


7.372 


5.162 


8.192 


5.736 


55 


15 


4.900 


3.463 


5.716 


4.040 


6.533 


4.617 


7.350 


5.194 


8.166 


5.772 


45 


30 


4.885 


3.484 


5.699 


4.065 


6.513 


4.646 


7.327 


5.226 


8.141 


5.807 


30 


45 


4.869 


3.505 


5.681 


4.090 


6.493 


4.674 


7.304 


5.258 


8.116 


5.843 


15 


36 


4.854 


3.527 


5.663 


4.115 


6.472 


4.702 


7.281 


5.290 


8.090 


5.878 


54 


15 


4.839 


3.548 


5.645 


4.139 


6.452 


4.730 


7.258 


5.322 


8.064 


5.913 


45 


30 


4.823 


3.569 


5.627 


4.164 


6.431 


4.759 


7.235 


5.353 


8.039 


5.948 


30 


45 


4.808 


3.590 


5.609 


4.188 


6.410 


4.787 


7.211 


5.385 


8.013 


5.983 


15 


37 


4.792 


3.611 


5.590 


4.213 


6.389 


4.815 


7.188 


5.416 


7.986 


6.018 


53 


15 


4.776 


3.632 


5.572 


4.237 


6.368 


4.842 


7.164 


5.448 


7.960 


6.053 


45 


30 


4.760 


3.653 


5.554 


4.261 


6.347 


4.870 


7.140 


5.479 


7.934 


6.088 


30 


45 


4.744 


3.673 


5.535 


4.286 


6.326 


4.898 


7.116 


5.510 


7.907 


6.122 


15 


38 


4.728 


3.694 


5.516 


4.310 


6 304 


4.925 


7.092 


5.541 


7.880 


6.157 


52 


15 


4.712 


3.715 


5.497 


4.334 


6.283 


4.953 


7.068 


5.572 


7.853 


6.191 


45 


30 


4.696 


3.735 


5.478 


4.358 


6.261 


4.980 


7.043 


5.603 


7.826 


6.225 


30 


45 


4.679 


3.756 


5.459 


4.381 


6.239 


5.007 


7.019 


5.633 


7.799 


6.259 


15 


39 


4.663 


3.776 


5.440 


4.405 


6.217 


5.035 


6.994 


5.664 


7.772 


6.293 


51 


15 


4.646 


3.796 


5.421 


4.429 


6.195 


5.062 


6.970 


5.694 


7.744 


6.327 


45 


30 


4.630 


3.816 


5.401 


4.453 


6.173 


5.089 


6.945 


5.725 


7.716 


6.361 


30 


45 


4.613 


3.837 


5.382 


4.476 


6.151 


5.116 


6.920 


5.755 


7.688 


6.394 


15 


40 


4.596 


3.857 


5.362 


4.500 


6.128 


5.142 


6.894 


5.785 


7.660 


6.428 


50 


15 


4.579 


3.877 


5.343 


4.523 


6.106 


5.169 


6.869 


5.815 


7.632 


6.461 


45 


30 


4.562 


3.897 


5.323 


4.546 


6.083 


5.196 


6.844 


5.845 


7.604 


6.495 


30 


45 


4.545 


3.917 


5.303 


4.569 


6.061 


5.222 


6.818 


5.875 


7.576 


6.528 


15 


41 


4.528 


3.936 


5.283 


4.592 


6.038 


5.248 


6.792 


5.905 


7.547 


6.561 


49 


15 


4.511 


3.956 


5263 


4.615 


6.0.15 


5.275 


6.767 


5.934 


7.518 


6.594 


45 


30 


4.494 


3.976 


5.243 


4 638 


5.992 


5.301 


6.741 


5.964 


7.490 


6.626 


30 


45 


4.476 


3.995 


5.222 


4.661 


5.968 


5.327 


6.715 


5.993 


7.461 


6.659 


15 


42 


4.459 


4.015 


5.202 


4.684 


5.945 


5.353 


6.688 


6022 


7.431 


6.691 


48 


15 


4.441 


4.034 


5.182 


4.707 


5.922 


5.379 


6.662 


6.051 


7.402 


6.724 


45 


30 


4.424 


4.054 


5.161 


4.729 


5.898 


5.405 


6.635 


6080 


7.373 


6.756 


30 


45 


4.406 


4.073 


5.140 


4.752 


5.875 


5.430 


6.609 


6.109 


7.343 


6.788 


15 


43 


4.388 


4.092 


5.119 


4.774 


5.851 


5.456 


6.582 


6.138 


7.314 


6.820 


47 


15 


4.370 


4.111 


5.099 


4.796 


5.827 


5.481 


6.555 


6.167 


7.284 


6.852 


45 


30 


4.352 


4.130 


5.078 


4.818 


5.803 


5.507 


6.528 


6.195 


7.254 


6884 


30 


45 


4.334 


4.149 


5.057 


4.841 


5.779 


5.532 


6.501 


6 224 


7.224 


6.915 


15 


44 


4.316 


4.168 


5.035 


4.863 


5.755 


5.557 


6.474 


6.252 


7.193 


6.947 


46 


15 


4.298 


4.187 


5.014 


4.885 


5.730 


5.582 


6.447 


6.280 


7.163 


6.978 


45 


30 


4.280 


4.206 


4.993 


4.906 


5.706 


5.607 


6.419 


6.308 


7.133 


7.009 


30 


45 


4.261 


4.224 


4.971 


4.928 


5.681 


5.632 


6.392 


6.336 


7.102 


7.040 


15 


45 


4.243 


4.243 


4.950 


4.950 


5.657 


5.657 


6.364 


6.364 , 


7.071 


7.071 


45 


o t 


Dep, 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat, 


Dep. 


Lat. 


o t 


Bearing, 


Distance 6. 


Distance 7. 


Distance 8. 


Distance 9. ] 


Distance 10. 


Bearing. 



45°-60 c 




A TABLE OF THE ANGLES 

Which every Point and Quarter Point of the Compass makes with the Meridian. 



North.. 


Points. 

0-14 

o- 1 ! 
0-% 
1 


t 11 

2 48 45 

5 37 30 

8 26 15 

11 15 


Points. 

o-i| 

0-34* 


South.. 


N. by E. 


N. by W. 


S. by E. 


S. by W. 


N.N.E. 


N.N.W. 


1-% 

1-34 
2 


14 3 45 
16 52 30 
19 41 15 
22 30 


I-V4 
I-V2 
l-3/ 4 
2 


S.S.E. 


S.S.W. 


N.E. by N. 


N.W. by N. 


2-1/4 
2-V2 
2-34 
3 


25 18 45 
28. 7 30 
30 56 15 
33 45 


2-V4 
2-V2 
2-% 
3 


S.E. by S. 


S.W. by S. 


NE. 


N.W. 


3-% 

3-i| 
3- 3 i 
4 


36 33 45 
39 22 30 
42 11 15 
45 


3-1/4 
8-« 
3-3/ 4 
4 


S.E. 


S.W. 


N.E. by E 


N.W.byW. 


4-1/4 
4-i/ 2 
4-% 
5 


47 48 45 
50 37 30 
53 26 15 
56 15 


4-% 
5 


S.E. by E. 


S.W. by W. 


E.N.E. 


W.N.W. 


5-V4 
5- 1 ! 
6-% 
6 


59 3 45 
61 52 30 
64 41 15 
67 30 


5-V4 

5-% 
6 


E.S.E. 


W.S.W. 


E. by N. 


W. by N. 


6-y 4 

6-% 
6-% 
7 


70 18 45 
73 7 30 
75 56 15 
78 45 


6-V4 
6-i| 

«-% 

7 


E. by S. 


W. by S. 


East. 


West. 




81 33 45 
84 22 30 
87 11 15 
90 


7-i/ 4 
7-V, 

r-% 

8 


East. 


West. 



iPR 15 1903 



WtVi 



LIBKAHY Ul- UUNtiKCSS 



020 186 234 6 







